On the public citation graph
Shape optimization for Dirichlet problems: Relaxed formulation and optimality conditions
0 signed · 148 inferred · view as graph
Inferred edges come from two machine sources: sweeps of open repository metadata (mostly SSRN and Zenodo), and a bulk OpenAlex citation snapshot. Every row below is labelled with the one it came from. Neither is a complete citation index — absence here is not evidence of absence.
Is this your work? Sign in with ORCID and put your name on the
claims that are yours.
Reference health. See whether every reference in this work resolves to a
known work and none has been retracted — and get a dated CiteStamped
badge you can embed.
What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1002/cpa.3160390107openalex-snapshot
Optimal design and relaxation of variational problems, I
inferredcites →https://doi.org/10.1002/cpa.3160400605openalex-snapshot
Relaxation of a variational method for impedance computed tomography
inferredcites →https://doi.org/10.1007/3-540-07623-9_279openalex-snapshot
Etude de problemes d'optimal design
inferredcites →https://doi.org/10.1007/978-1-4471-5102-9openalex-snapshot
Encyclopedia of Systems and Control
inferredcites →https://doi.org/10.1007/978-1-4612-5208-5openalex-snapshot
Classical Potential Theory and Its Probabilistic Counterpart
inferredcites →https://doi.org/10.1007/978-3-642-46317-4_30openalex-snapshot
Problemes de Controle des Coefficients Dans des Equations aux Derivees Partielles
inferredcites →https://doi.org/10.1007/978-3-642-56573-1openalex-snapshot
Classical Potential Theory and Its Probabilistic Counterpart
inferredcites →https://doi.org/10.1007/978-3-642-87722-3openalex-snapshot
Optimal Shape Design for Elliptic Systems
inferredcites →https://doi.org/10.1007/978-94-009-8606-0_10openalex-snapshot
Problems of Shape Optimal Design
inferredcites →https://doi.org/10.1007/978-94-009-8606-0_12openalex-snapshot
The Material Derivative (or Speed) Method for Shape Optimization
inferredcites →https://doi.org/10.1007/bf00276841openalex-snapshot
Wiener criteria and energy decay for relaxed dirichlet problems
inferredcites →https://doi.org/10.1007/bf01442645openalex-snapshot
Wiener's criterion and Γ-convergence
inferredcites →https://doi.org/10.1007/bf02385982openalex-snapshot
Two approximation problems in function spaces
inferredcites →https://doi.org/10.1007/bfb0060353openalex-snapshot
On Topologies and Boundaries in Potential Theory
inferredcites →https://doi.org/10.1007/bfb0066246openalex-snapshot
Mathematical Theories of Optimization
inferredcites →https://doi.org/10.1080/03605307908820120openalex-snapshot
A property of sobolev spaces
inferredcites →https://doi.org/10.1090/s0002-9947-1987-0896006-7openalex-snapshot
Stopping Times and Γ-Convergence
inferredcites →https://doi.org/10.1090/s0273-0979-1990-15971-3openalex-snapshot
Shape optimization for Dirichlet problems: Relaxed solutions and optimality conditions
inferredcites →https://doi.org/10.1137/1.9780898719451openalex-snapshot
An Introduction to Variational Inequalities and Their Applications
inferredcites →https://doi.org/10.1512/iumj.1973.22.22013openalex-snapshot
The Lebesgue Set of a Function whose Distribution Derivatives are p-th Power Summable
inferredcites →https://doi.org/10.2307/2314669openalex-snapshot
Variational Methods for the Study of Nonlinear Operators
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.1006/jdeq.1998.3497openalex-snapshot
Characterization for the Kuratowski Limits of a Sequence of Sobolev Spaces
inferred← citeshttps://doi.org/10.1006/jfan.1997.3130openalex-snapshot
Manifold Derivative in the Laplace–Beltrami Equation
inferred← citeshttps://doi.org/10.1006/jfan.1998.3363openalex-snapshot
An Existence Result for Optimal Obstacles
inferred← citeshttps://doi.org/10.1007/978-0-8176-8089-3_20openalex-snapshot
Measure-Valued Solutions to a Harvesting Game with Several Players
inferred← citeshttps://doi.org/10.1007/978-1-4612-2032-9openalex-snapshot
Topics in the Mathematical Modelling of Composite Materials
inferred← citeshttps://doi.org/10.1007/978-1-4613-0287-2_5openalex-snapshot
A Survey on Optimal Shape Design Problems for Systems Described by Partial Differential Equations and Hemivariational Inequalities
inferred← citeshttps://doi.org/10.1007/978-3-031-04616-2_11openalex-snapshot
Uniqueness and Stability in an Inverse Problem for Electromagnetic Forming of a Metal Jet
inferred← citeshttps://doi.org/10.1007/978-3-319-05083-6_13openalex-snapshot
Two-Stage Stochastic Optimization Meets Two-Scale Simulation
inferred← citeshttps://doi.org/10.1007/978-3-319-17563-8_2openalex-snapshot
Optimization Problems Involving the First Dirichlet Eigenvalue and the Torsional Rigidity
inferred← citeshttps://doi.org/10.1007/978-3-319-90469-6_2openalex-snapshot
Homogenization of Stochastic Parabolic Equations in Varying Domains
inferred← citeshttps://doi.org/10.1007/978-3-319-97184-1openalex-snapshot
Topics in the Mathematical Modelling of Composite Materials
inferred← citeshttps://doi.org/10.1007/978-3-540-44857-0_2openalex-snapshot
Optimal Shapes and Masses, and Optimal Transportation Problems
inferred← citeshttps://doi.org/10.1007/978-3-8348-9396-3openalex-snapshot
Shape Optimization under Uncertainty from a Stochastic Programming Point of View
inferred← citeshttps://doi.org/10.1007/978-88-7642-527-1openalex-snapshot
Existence and Regularity Results for Some Shape Optimization Problems
inferred← citeshttps://doi.org/10.1007/978-94-011-1804-0_24openalex-snapshot
Existence Via Relaxation for Some Domain Optimization Problems
inferred← citeshttps://doi.org/10.1007/978-94-011-4560-2_3openalex-snapshot
Relaxed optimal control problems and applications to shape optimization
inferred← citeshttps://doi.org/10.1007/b12016openalex-snapshot
Optimal Transportation and Applications
inferred← citeshttps://doi.org/10.1007/bf00378167openalex-snapshot
An existence result for a class of shape optimization problems
inferred← citeshttps://doi.org/10.1007/bf01759320openalex-snapshot
Comparison results for some types of relaxation of variational integral functionals
inferred← citeshttps://doi.org/10.1007/bf02367274openalex-snapshot
Generalized implicit function theorems and problems with a free boundary
inferred← citeshttps://doi.org/10.1007/bf02788033openalex-snapshot
A capacitary method for the asymptotic analysis of dirichlet problems for monotone operators
inferred← citeshttps://doi.org/10.1007/bfb0006687openalex-snapshot
Relaxed formulation for a class of shape optimization problems
inferred← citeshttps://doi.org/10.1007/s00028-012-0144-4openalex-snapshot
Domain perturbation and invariant manifolds
inferred← citeshttps://doi.org/10.1007/s00030-004-2025-1openalex-snapshot
Relaxed Dirichlet problem and shape optimization within the linear elasticity framework
inferred← citeshttps://doi.org/10.1007/s00033-003-3204-3openalex-snapshot
On the isoperimetric inequality for the buckling of a clamped plate
inferred← citeshttps://doi.org/10.1007/s00205-008-0166-9openalex-snapshot
Quasistatic Evolution in Debonding Problems via Capacitary Methods
inferred← citeshttps://doi.org/10.1007/s00205-014-0801-6openalex-snapshot
Lipschitz Regularity of the Eigenfunctions on Optimal Domains
inferred← citeshttps://doi.org/10.1007/s00205-015-0934-2openalex-snapshot
Extremality Conditions and Regularity of Solutions to Optimal Partition Problems Involving Laplacian Eigenvalues
inferred← citeshttps://doi.org/10.1007/s00245-006-0856-3openalex-snapshot
Optimal Measures for Nonlinear Cost Functionals
inferred← citeshttps://doi.org/10.1007/s00245-013-9222-4openalex-snapshot
Existence and Regularity of Minimizers for Some Spectral Functionals with Perimeter Constraint
inferred← citeshttps://doi.org/10.1007/s00245-015-9291-7openalex-snapshot
Shape and Topology Optimization in Stokes Flow with a Phase Field Approach
inferred← citeshttps://doi.org/10.1007/s00245-025-10286-yopenalex-snapshot
Approximation and Characterization of Elastic Relaxed Dirichlet Problems and Shape Optimization
inferred← citeshttps://doi.org/10.1007/s00526-011-0441-8openalex-snapshot
On the characterization of the compact embedding of Sobolev spaces
inferred← citeshttps://doi.org/10.1007/s00526-021-02011-8openalex-snapshot
Optimization of the principal eigenvalue for elliptic operators
inferred← citeshttps://doi.org/10.1007/s10231-005-0151-yopenalex-snapshot
Optimal measures for elliptic problems
inferred← citeshttps://doi.org/10.1007/s10915-006-9114-8openalex-snapshot
An Optimal Partition Problem for Eigenvalues
inferred← citeshttps://doi.org/10.1007/s10957-018-1347-9openalex-snapshot
Optimal Potentials for Problems with Changing Sign Data
inferred← citeshttps://doi.org/10.1007/s11228-019-0506-yopenalex-snapshot
Generalized Derivatives for the Solution Operator of the Obstacle Problem
inferred← citeshttps://doi.org/10.1007/s11425-020-1802-6openalex-snapshot
Large m asymptotics for minimal partitions of the Dirichlet eigenvalue
inferred← citeshttps://doi.org/10.1007/s13163-011-0066-7openalex-snapshot
Spectral optimization problems
inferred← citeshttps://doi.org/10.1007/s13398-024-01662-4openalex-snapshot
Control problems in the coefficients and the domain for linear elliptic equations
inferred← citeshttps://doi.org/10.1007/s41808-025-00414-8openalex-snapshot
A non-existence result for the reinforced membrane problem
inferred← citeshttps://doi.org/10.1016/j.anihpc.2003.05.001openalex-snapshot
Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains
inferred← citeshttps://doi.org/10.1016/j.anihpc.2007.07.004openalex-snapshot
Nodal domains and spectral minimal partitions
inferred← citeshttps://doi.org/10.1016/j.anihpc.2012.10.002openalex-snapshot
Spectral optimization problems with internal constraint
inferred← citeshttps://doi.org/10.1016/j.apnum.2009.01.008openalex-snapshot
Topological optimization method for a geometric control problem in Stokes flow
inferred← citeshttps://doi.org/10.1016/j.cam.2005.04.047openalex-snapshot
Homogenization of Dirichlet parabolic problems for coefficients and open sets simultaneously variable and applications to optimal design
inferred← citeshttps://doi.org/10.1016/j.camwa.2025.03.012openalex-snapshot
Topology optimization of Stokes eigenvalues by a level set method
inferred← citeshttps://doi.org/10.1016/j.cnsns.2025.108854openalex-snapshot
Topology optimization of the two smallest p -Laplacian eigenvalues by a level set method
inferred← citeshttps://doi.org/10.1016/j.jfa.2012.09.017openalex-snapshot
Shape optimization problems on metric measure spaces
inferred← citeshttps://doi.org/10.1016/j.jmaa.2004.07.042openalex-snapshot
A domain optimization problem with boundary penalty cost functional
inferred← citeshttps://doi.org/10.1016/j.jmaa.2022.126648openalex-snapshot
Singular geometry perturbation based method for shape-topology optimization in unsteady Stokes flow
inferred← citeshttps://doi.org/10.1016/j.matpur.2007.12.010openalex-snapshot
Asymptotic behaviour of contact problems between two elastic materials through a fractal interface
inferred← citeshttps://doi.org/10.1016/j.matpur.2020.08.004openalex-snapshot
Measure valued solutions for an optimal harvesting problem
inferred← citeshttps://doi.org/10.1016/j.na.2016.05.014openalex-snapshot
Worst-case shape optimization for the Dirichlet energy
inferred← citeshttps://doi.org/10.1016/j.nonrwa.2015.09.009openalex-snapshot
Existence analysis of an optimal shape design problem with non coercive state equation
inferred← citeshttps://doi.org/10.1016/s0021-7824(02)01256-4openalex-snapshot
Domain perturbations and estimates for the solutions of second order elliptic equations
inferred← citeshttps://doi.org/10.1016/s0022-0396(02)00105-5openalex-snapshot
Dirichlet problems on varying domains
inferred← citeshttps://doi.org/10.1016/s1007-5704(03)00098-4openalex-snapshot
An existence result for control problems on the coefficients and the domain for nonlinear parabolic Dirichlet problems
inferred← citeshttps://doi.org/10.1016/s1874-5733(08)80018-6openalex-snapshot
Domain Perturbation for Linear and Semi-Linear Boundary Value Problems
inferred← citeshttps://doi.org/10.1017/s0004972711002930openalex-snapshot
DOMAIN PERTURBATION FOR PARABOLIC EQUATIONS
inferred← citeshttps://doi.org/10.1017/s0308210500030006openalex-snapshot
Shape optimisation problems governed by nonlinear state equations
inferred← citeshttps://doi.org/10.1051/cocv/2015006openalex-snapshot
Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow
inferred← citeshttps://doi.org/10.1051/cocv/2022090openalex-snapshot
Phase-field methods for spectral shape and topology optimization
inferred← citeshttps://doi.org/10.1051/cocv:2004016openalex-snapshot
The topological asymptotic expansion for the Quasi-Stokes problem
inferred← citeshttps://doi.org/10.1051/cocv:2006020openalex-snapshot
Asymptotics of an optimal compliance-location problem
inferred← citeshttps://doi.org/10.1051/cocv:2007045openalex-snapshot
Removing holes in topological shape optimization
inferred← citeshttps://doi.org/10.1051/cocv:2008069openalex-snapshot
Optimal measures for the fundamental gap of Schrödinger operators
inferred← citeshttps://doi.org/10.1051/m2an/2017004openalex-snapshot
A posteriorimodeling error estimates in the optimization of two-scale elastic composite materials
inferred← citeshttps://doi.org/10.1051/proc:1998039openalex-snapshot
On the existence of minimizing domains for some shape optimization problems
inferred← citeshttps://doi.org/10.1080/00207160701199765openalex-snapshot
Homogenization of nonlinear parabolic problems with varying boundary conditions on varying sets
inferred← citeshttps://doi.org/10.1080/03605309608821222openalex-snapshot
Asymptotic behaviour of dirichlet problems with measure data in perforated domains
inferred← citeshttps://doi.org/10.1088/0951-7715/22/1/005openalex-snapshot
Numerical approximations of a norm-preserving gradient flow and applications to an optimal partition problem
inferred← citeshttps://doi.org/10.1090/qam/1464openalex-snapshot
Optimal shape design in three-dimensional Brinkman flow using asymptotic analysis techniques
inferred← citeshttps://doi.org/10.1090/s0273-0979-99-00774-0openalex-snapshot
Optimization, relaxation and Young measures
inferred← citeshttps://doi.org/10.1090/s0894-0347-08-00593-6openalex-snapshot
Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries
inferred← citeshttps://doi.org/10.1134/s0005117907020075openalex-snapshot
Boundary control of a laminar flow of a viscous incompressible fluid in the generalized Couette cell. The asymptotic approach
inferred← citeshttps://doi.org/10.1137/050631720openalex-snapshot
From Differential Calculus to 0‐1 Topological Optimization
inferred← citeshttps://doi.org/10.1137/120880173openalex-snapshot
Geometrical Structure of Laplacian Eigenfunctions
inferred← citeshttps://doi.org/10.1137/130904600openalex-snapshot
Electrostatic Forces on Charged Surfaces of Bilayer Lipid Membranes
inferred← citeshttps://doi.org/10.1137/130917272openalex-snapshot
Multiphase Shape Optimization Problems
inferred← citeshttps://doi.org/10.1137/130939808openalex-snapshot
Spectral Optimization Problems for Potentials and Measures
inferred← citeshttps://doi.org/10.1137/17m1126564openalex-snapshot
A Shape Optimal Control Problem with Changing Sign Data
inferred← citeshttps://doi.org/10.1137/18m1192949openalex-snapshot
On the Competitive Harvesting of Marine Resources
inferred← citeshttps://doi.org/10.1137/19m1287006openalex-snapshot
On the Existence of Optimal Potentials on Unbounded Domains
inferred← citeshttps://doi.org/10.1137/23m161553xopenalex-snapshot
Spectral Partition Problems with Volume and Inclusion Constraints
inferred← citeshttps://doi.org/10.1137/s0036141002389579openalex-snapshot
A Duality Approach for the Boundary Variation of Neumann Problems
inferred← citeshttps://doi.org/10.1137/s0036141097329135openalex-snapshot
On The Attainable Eigenvalues of the Laplace Operator
inferred← citeshttps://doi.org/10.1137/s0036141097329627openalex-snapshot
Asymptotic Behavior of Nonlinear Elliptic Systems on Varying Domains
inferred← citeshttps://doi.org/10.1137/s0363012901384193openalex-snapshot
The Topological Asymptotic Expansion for the Dirichlet Problem
inferred← citeshttps://doi.org/10.1137/s0363012902406801openalex-snapshot
The Topological Asymptotic for the Helmholtz Equation
inferred← citeshttps://doi.org/10.1137/s0363012902411210openalex-snapshot
Topological Sensitivity and Shape Optimization for the Stokes Equations
inferred← citeshttps://doi.org/10.1186/s13640-019-0456-1openalex-snapshot
Mice endplate segmentation from micro-CT data through graph-based trabecula recognition
inferred← citeshttps://doi.org/10.1186/s13661-022-01592-3openalex-snapshot
Kohn–Vogelius formulation for plasma geometry identification problem
inferred← citeshttps://doi.org/10.12775/tmna.2000.036openalex-snapshot
Existence and relaxation problems in optimal shape design
inferred← citeshttps://doi.org/10.1515/acv-2023-0010openalex-snapshot
On the regularity of optimal potentials in control problems governed by elliptic equations
inferred← citeshttps://doi.org/10.1515/acv.2010.013openalex-snapshot
On some rescaled shape optimization problems
inferred← citeshttps://doi.org/10.2139/ssrn.7200738openalex-snapshot
Geometric Identification of Initial Velocity Perturbation Supports in the Navier–Stokes Equations Via Topological Gradient: Application to Mediterranean Sea Circulation
inferred← citeshttps://doi.org/10.3233/asy-2000-399openalex-snapshot
Wave equation in domains with many small obstacles
inferred← citeshttps://doi.org/10.3233/asy-2008-0871openalex-snapshot
Homogenization of Dirichlet optimal control problems with exact partial controllability constraints
inferred← citeshttps://doi.org/10.3934/dcdsb.2015.20.2967openalex-snapshot
Shape stability of optimal control problems in coefficients for coupled system of Hammerstein type
inferred← citeshttps://doi.org/10.3934/dcdss.2016055openalex-snapshot
A posteriori error estimates for sequential laminates in shape optimization
inferred← citeshttps://doi.org/10.4171/ifb/248openalex-snapshot
Analysis and simulation of debonding membranes
inferred← citeshttps://doi.org/10.4171/rlm/942openalex-snapshot
Shape optimization problems in control form
inferred← citeshttps://doi.org/10.46298/cm.12568openalex-snapshot
Topics in elliptic problems: from semilinear equations to shape optimization
inferred← citeshttps://doi.org/10.46300/91018.2022.9.2openalex-snapshot
Approximation of a Wanted Flow via Topological Sensitivity Analysis
inferred← citeshttps://doi.org/10.48550/arxiv.1012.3299openalex-snapshot
Spectral Optimization Problems
inferred← citeshttps://doi.org/10.48550/arxiv.1109.2413openalex-snapshot
Shape Optimization Problems with Internal Constraint
inferred← citeshttps://doi.org/10.48550/arxiv.1305.0406openalex-snapshot
Optimal Potentials For Schrodinger Operators
inferred← citeshttps://doi.org/10.48550/arxiv.1310.1568openalex-snapshot
Spectral optimization problems for potentials and measures
inferred← citeshttps://doi.org/10.48550/arxiv.1310.2448openalex-snapshot
Multiphase shape optimization problems
inferred← citeshttps://doi.org/10.48550/arxiv.1407.5470openalex-snapshot
Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow
inferred← citeshttps://doi.org/10.48550/arxiv.1511.04329openalex-snapshot
A posteriori modeling error estimates in the optimization of two-scale elastic composite materials
inferred← citeshttps://doi.org/10.48550/arxiv.math/0006009openalex-snapshot
Asymptotic behaviour of solutions of fourth order Dirichlet problems
inferred← citeshttps://doi.org/10.48550/arxiv.math/0205225openalex-snapshot
Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains
inferred← citeshttps://doi.org/10.48550/arxiv.math/0503426openalex-snapshot
Asymptotics of an optimal compliance-location problem
inferred← citeshttps://doi.org/10.48550/arxiv.math/0703734openalex-snapshot
Variational problems on classes of convex domains
inferred← citeshttps://doi.org/10.57262/ade/1355854622openalex-snapshot
Asymptotic analysis for some linear eigenvalue problems via Gamma-Convergence
inferred← citeshttps://doi.org/10.5772/26926openalex-snapshot
Topology Optimization of Fluid Mechanics Problems
inferred← citeshttps://doi.org/10.5802/afst.761openalex-snapshot
Completion by Gamma-convergence for optimal control problems
inferred← citeshttps://doi.org/10.5802/jep.4openalex-snapshot
Optimal potentials for Schrödinger operators
inferred← citeshttps://doi.org/10.68381/jca11002openalex-snapshot
A Duality Approach for Variational Problems in Domains with Cracks
Editorial review for independent work. ICSAC — the Institute for Complexity
Science and Advanced Computing — runs a structured editorial panel for researchers
publishing outside journals, and publishes on CiteStamp rails. Submission is free
and goes through ORCID: icsacinstitute.org/submit.