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Convex solutions of certain elliptic equations have constant rank hessians

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inferredcites →https://doi.org/10.1002/mma.1670080107openalex-snapshot
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inferredcites →https://doi.org/10.1007/978-3-642-61798-0openalex-snapshot
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inferredcites →https://doi.org/10.1007/978-3-642-96379-7openalex-snapshot
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inferredcites →https://doi.org/10.1007/bf01180586openalex-snapshot
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inferredcites →https://doi.org/10.1112/jlms/s1-32.3.286openalex-snapshot
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inferredcites →https://doi.org/10.1215/s0012-7094-85-05221-4openalex-snapshot
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inferredcites →https://doi.org/10.1512/iumj.1983.32.32042openalex-snapshot
inferredcites →https://doi.org/10.1512/iumj.1985.34.34036openalex-snapshot

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inferred← citeshttps://doi.org/10.1002/(sici)1099-1476(200002)23:3<255::aid-mma113>3.0.co;2-5openalex-snapshot
Isoperimetric inequalities for the energy of uniform-vorticity flows in channels of uniform width
inferred← citeshttps://doi.org/10.1002/cpa.20118openalex-snapshot
The Christofel‐Minkowski problem III: Existence and convexity of admissible solutions
inferred← citeshttps://doi.org/10.1002/cpa.20197openalex-snapshot
A constant rank theorem for solutions of fully nonlinear elliptic equations
inferred← citeshttps://doi.org/10.1002/mma.11198openalex-snapshot
Geometrical Properties of Solutions to −Δgu=f(u)$$ -{\Delta}_gu=f(u) $$
inferred← citeshttps://doi.org/10.1007/978-1-4612-4656-5_13openalex-snapshot
Convexity Properties of Solutions to Elliptic P.D.E.’S
inferred← citeshttps://doi.org/10.1007/978-1-4613-8357-4_2openalex-snapshot
Convex Free Boundaries and the Operator Method
inferred← citeshttps://doi.org/10.1007/978-3-030-38230-8_16openalex-snapshot
Geometric properties of superlevel sets of semilinear elliptic equations in convex domains
inferred← citeshttps://doi.org/10.1007/978-3-319-76666-9_2openalex-snapshot
The Carleman Inequality for Linear Parabolic Equations
inferred← citeshttps://doi.org/10.1007/978-3-319-76666-9_3openalex-snapshot
Exact Controllability of Parabolic Equations
inferred← citeshttps://doi.org/10.1007/978-88-470-2841-8_3openalex-snapshot
Power Concavity for Solutions of Nonlinear Elliptic Problems in Convex Domains
inferred← citeshttps://doi.org/10.1007/bf00945002openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/bf00946255openalex-snapshot
Asymptotic behavior of positive solution branches of elliptic problems with linear part at resonance
inferred← citeshttps://doi.org/10.1007/bf02567439openalex-snapshot
Uniqueness of least energy solutions to a semilinear elliptic equation in ℝ2
inferred← citeshttps://doi.org/10.1007/pl00005534openalex-snapshot
Symmetry Breaking and Other Phenomena in the Optimization of Eigenvalues for Composite Membranes
inferred← citeshttps://doi.org/10.1007/s00033-002-8163-6openalex-snapshot
inferred← citeshttps://doi.org/10.1007/s00033-012-0217-9openalex-snapshot
A minimum principle for the problem of St-Venant in $${\mathbb{R}^N, N \geq 2}$$
inferred← citeshttps://doi.org/10.1007/s00205-022-01759-3openalex-snapshot
On Concavity of Solutions of the Nonlinear Poisson Equation
inferred← citeshttps://doi.org/10.1007/s00208-011-0729-1openalex-snapshot
A maximum rank problem for degenerate elliptic fully nonlinear equations
inferred← citeshttps://doi.org/10.1007/s00208-023-02722-7openalex-snapshot
On the critical points of semi-stable solutions on convex domains of Riemannian surfaces
inferred← citeshttps://doi.org/10.1007/s00220-012-1508-xopenalex-snapshot
From the Ginzburg-Landau Model to Vortex Lattice Problems
inferred← citeshttps://doi.org/10.1007/s00222-002-0259-2openalex-snapshot
The Christoffel-Minkowski problem I: Convexity of solutions of a Hessian equation
inferred← citeshttps://doi.org/10.1007/s00222-009-0179-5openalex-snapshot
A microscopic convexity principle for nonlinear partial differential equations
inferred← citeshttps://doi.org/10.1007/s00229-011-0485-2openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s00526-003-0250-9openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s00526-010-0333-3openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s00526-010-0379-2openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s00526-020-01897-0openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s00526-023-02442-5openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s00526-025-03125-zopenalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s10114-012-1495-zopenalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s10473-023-0310-5openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s10473-025-0111-0openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s11401-005-0575-0openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s11425-021-1957-7openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s11587-009-0058-9openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s12220-022-01186-6openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/s12220-026-02363-7openalex-snapshot
On Shape Optimization with Large Magnetic Fields in Two Dimensions
inferred← citeshttps://doi.org/10.1016/j.aim.2004.06.002openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.aim.2010.04.003openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.aim.2011.12.009openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.aim.2014.01.024openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.aim.2015.01.012openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.aim.2026.110827openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.jde.2005.08.005openalex-snapshot
Translating solitons of mean curvature flow of noncompact spacelike hypersurfaces in Minkowski space
inferred← citeshttps://doi.org/10.1016/j.jde.2011.12.010openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.jde.2022.01.046openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.jde.2024.12.004openalex-snapshot
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inferred← citeshttps://doi.org/10.1016/j.jde.2025.113452openalex-snapshot
Concavity and perturbed concavity for p-Laplace equations
inferred← citeshttps://doi.org/10.1016/j.jfa.2008.06.008openalex-snapshot
The convexity of solution of a class Hessian equation in bounded convex domain in R3
inferred← citeshttps://doi.org/10.1016/j.jfa.2025.110935openalex-snapshot
Two new constant rank theorems
inferred← citeshttps://doi.org/10.1016/j.jmaa.2014.01.046openalex-snapshot
Convexity estimates for the solutions of a class of semi-linear elliptic equations
inferred← citeshttps://doi.org/10.1016/j.matpur.2019.01.013openalex-snapshot
Monotone properties of the eigenfunction of Neumann problems
inferred← citeshttps://doi.org/10.1016/j.na.2013.02.002openalex-snapshot
Power convexity of a class of elliptic equations involving the Hessian operator in a 3-dimensional bounded convex domain
inferred← citeshttps://doi.org/10.1016/j.na.2023.113353openalex-snapshot
Superharmonic functions related to convexity estimates for a class of semilinear elliptic problems
inferred← citeshttps://doi.org/10.1016/s0304-0208(08)70510-3openalex-snapshot
Uniqueness of Critical Point of the Solution to the Prescribed Constant Mean Curvature Equation Over Convex Domain in R2
inferred← citeshttps://doi.org/10.1016/s0377-0427(96)00152-5openalex-snapshot
A trial-free-boundary method for computing Batchelor flows
inferred← citeshttps://doi.org/10.1016/s1874-5733(04)80005-6openalex-snapshot
Qualitative Properties of Solutions to Elliptic Problems
inferred← citeshttps://doi.org/10.1051/cocv/2017069openalex-snapshot
On two functionals involving the maximum of the torsion function
inferred← citeshttps://doi.org/10.1080/00036810500277819openalex-snapshot
Brunn-Minkowski inequalities for two functionals involving thep-Laplace operator
inferred← citeshttps://doi.org/10.1080/03605302.2012.727129openalex-snapshot
The Convexity Estimates for the Solutions of Two Elliptic Equations
inferred← citeshttps://doi.org/10.1080/03605302.2021.1892755openalex-snapshot
Weak Harnack inequalities for eigenvalues and constant rank theorems
inferred← citeshttps://doi.org/10.1080/03605308908820634openalex-snapshot
A counterexample to the convexity property of the first eigenfunction on a convex domain of negative curvature
inferred← citeshttps://doi.org/10.1080/03605309108820828openalex-snapshot
Lewy's harmonic gradient maps in higher dimensions
inferred← citeshttps://doi.org/10.1080/03605309908820698openalex-snapshot
Conexity Of Level Sets For Solutions To elliptic Ring Problems
inferred← citeshttps://doi.org/10.1080/17476933.2018.1533000openalex-snapshot
The concavity region of solutions to the Poisson equation in the plane
inferred← citeshttps://doi.org/10.1081/pde-200037754openalex-snapshot
Some Results for the Gelfand's Problem
inferred← citeshttps://doi.org/10.1090/memo/1244openalex-snapshot
On Space-Time Quasiconcave Solutions of the Heat Equation
inferred← citeshttps://doi.org/10.1090/proc/12969openalex-snapshot
Entire downward translating solitons to the mean curvature flow in Minkowski space
inferred← citeshttps://doi.org/10.1090/proc/16028openalex-snapshot
Constant rank theorems for Li-Yau-Hamilton type matrices of heat equations
inferred← citeshttps://doi.org/10.1090/proc/17590openalex-snapshot
Strong log-concavity for the first eigenfunction of the Ornstein-Uhlenbeck operator in the class of convex bodies
inferred← citeshttps://doi.org/10.1090/pspum/099/01744openalex-snapshot
The Dirichlet problem for the complex homogeneous Monge-Ampère equation
inferred← citeshttps://doi.org/10.1090/s0002-9939-1992-1086339-3openalex-snapshot
On Convexity of Level Curves of Harmonic Functions in the Hyperbolic Plane
inferred← citeshttps://doi.org/10.1090/s0002-9947-1990-1008702-1openalex-snapshot
Uniqueness of the critical point of the solutions to some semilinear elliptic boundary value problems in 𝑅²
inferred← citeshttps://doi.org/10.1090/s0002-9947-98-01943-6openalex-snapshot
On the existence of convex classical solutions for multilayer free boundary problems with general nonlinear joining conditions
inferred← citeshttps://doi.org/10.1090/tran/1998-350-08openalex-snapshot
inferred← citeshttps://doi.org/10.1090/tran/7049openalex-snapshot
The shape of the level sets of the first eigenfunction of a class of two-dimensional Schrödinger operators
inferred← citeshttps://doi.org/10.1093/imrn/rnp007openalex-snapshot
The Existence of Convex Body with Prescribed Curvature Measures
inferred← citeshttps://doi.org/10.1093/imrn/rny243openalex-snapshot
Counterexamples to Quasiconcavity for the Heat Equation
inferred← citeshttps://doi.org/10.1112/blms.12750openalex-snapshot
Concavity of solutions to semilinear equations in dimension two
inferred← citeshttps://doi.org/10.1137/0524052openalex-snapshot
Convexity of Solutions to Some Elliptic Partial Differential Equations
inferred← citeshttps://doi.org/10.1137/15100494xopenalex-snapshot
A Variational Method for Second Order Shape Derivatives
inferred← citeshttps://doi.org/10.1137/17m1153881openalex-snapshot
Uniform Level Set Estimates for Ground State Eigenfunctions
inferred← citeshttps://doi.org/10.1137/23m1624658openalex-snapshot
A Geometric Bound on the Lowest Magnetic Neumann Eigenvalue via the Torsion Function
inferred← citeshttps://doi.org/10.1353/ajm.2016.0012openalex-snapshot
Convexity of level sets for elliptic problems in convex domains or convex rings: Two counterexamples
inferred← citeshttps://doi.org/10.1360/n012017-00251openalex-snapshot
The microscopic convexity of level sets of solutions for elliptic and parabolic equations
inferred← citeshttps://doi.org/10.1512/iumj.2011.60.4222openalex-snapshot
A constant rank theorem for quasiconcave solutions of fully nonlinear partial differential equations
inferred← citeshttps://doi.org/10.1512/iumj.2021.70.8551openalex-snapshot
Strong space-time convexity and the heat equation
inferred← citeshttps://doi.org/10.1515/acv-2021-0100openalex-snapshot
Concavity properties for solutions to p-Laplace equations with concave nonlinearities
inferred← citeshttps://doi.org/10.1515/ans-2013-0305openalex-snapshot
On Explosive Solutions for a Class of Quasi-linear Elliptic Equations
inferred← citeshttps://doi.org/10.2140/apde.2019.12.493openalex-snapshot
On the maximal rank problem for the complex homogeneous Monge–Ampère equation
inferred← citeshttps://doi.org/10.2140/pjm.1992.152.291openalex-snapshot
Superharmonicity of curvatures for surfaces of constant mean curvature
inferred← citeshttps://doi.org/10.2140/pjm.1994.162.201openalex-snapshot
On the existence of convex classical solutions to multilayer fluid problems in arbitrary space dimensions
inferred← citeshttps://doi.org/10.2140/pjm.2010.245.255openalex-snapshot
A constant rank theorem for level sets of immersed hypersurfaces in ℝn+1with prescribed mean curvature
inferred← citeshttps://doi.org/10.2140/pjm.2017.288.489openalex-snapshot
A sharp height estimate for the spacelike constant mean curvature graph in the Lorentz–Minkowski space
inferred← citeshttps://doi.org/10.2140/pjm.2018.295.499openalex-snapshot
Convexity of level sets and a two-point function
inferred← citeshttps://doi.org/10.3934/dcds.2010.28.441openalex-snapshot
Properties of translating solutions to mean curvatureflow
inferred← citeshttps://doi.org/10.3934/dcds.2010.28.789openalex-snapshot
A structural condition for microscopic convexity principle
inferred← citeshttps://doi.org/10.3934/dcds.2014.34.3383openalex-snapshot
On the microscopic spacetime convexity principle of fully nonlinear parabolic equations I: Spacetime convex solutions
inferred← citeshttps://doi.org/10.3934/dcds.2016081openalex-snapshot
On a constant rank theorem for nonlinear elliptic PDEs
inferred← citeshttps://doi.org/10.3934/dcds.2024073openalex-snapshot
Concave solutions to Finsler $ p $-Laplace type equations
inferred← citeshttps://doi.org/10.4171/rlm/997openalex-snapshot
Uniqueness of the critical point for solutions of some p-Laplace equations in the plane
inferred← citeshttps://doi.org/10.4208/ata.oa-2021-0048openalex-snapshot
Weak Harnack Inequalities for Eigenvalues and the Monotonicity of Hessian's Rank
inferred← citeshttps://doi.org/10.4208/jms.v50n2.17.05openalex-snapshot
Power Concavity for Doubly Nonlinear Parabolic Equations
inferred← citeshttps://doi.org/10.4208/jms.v52n1.19.07openalex-snapshot
The Convexity of a Fully Nonlinear Operator and Its Related Eigenvalue Problem
inferred← citeshttps://doi.org/10.4310/cag.2008.v16.n3.a3openalex-snapshot
Estimates on the lower bound of the first gap
inferred← citeshttps://doi.org/10.4310/cjm.2021.v9.n1.a3openalex-snapshot
Concavity properties of solutions to Robin problems
inferred← citeshttps://doi.org/10.4310/jdg/1214445535openalex-snapshot
Gauss maps of spacelike constant mean curvature hypersurfaces of Minkowski space
inferred← citeshttps://doi.org/10.4310/maa.2009.v16.n2.a5openalex-snapshot
A Constant Rank Theorem for Hermitian $k$-Convex Solutions of Complex Laplace Equations
inferred← citeshttps://doi.org/10.48550/arxiv.1005.0241openalex-snapshot
A constant rank theorem for partial convex solutions of partial differential equations
inferred← citeshttps://doi.org/10.48550/arxiv.1011.4617openalex-snapshot
From the Ginzburg-Landau model to vortex lattice problems
inferred← citeshttps://doi.org/10.48550/arxiv.1309.2821openalex-snapshot
The J-flow and stability
inferred← citeshttps://doi.org/10.48550/arxiv.1403.5077openalex-snapshot
On the microscopic spacetime convexity principle for fully nonlinear parabolic equations I: Spacetime convex solutions
inferred← citeshttps://doi.org/10.57262/ade/1356651221openalex-snapshot
Uniqueness for semilinear elliptic problems: supercritical growth and domain geometry
inferred← citeshttps://doi.org/10.6092/unina/fedoa/3482openalex-snapshot
HESSIAN EQUATIONS, QUERMASSINTEGRALS AND SYMMETRIZATION
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