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Optimal Control for the Thermistor Problem

https://doi.org/10.1137/080736259
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Outgoing claims: the papers this work cites, builds on, or argues with.

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Interpolation for Function Spaces Related to Mixed Boundary Value Problems
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Semigroups of Linear Operators and Applications to Partial Differential Equations
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Analytic Semigroups and Optimal Regularity in Parabolic Problems
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Linear and Quasilinear Parabolic Problems
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Regularity and stability for the mathematical programming problem in Banach spaces
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Resolvent estimates inW −1,p for second order elliptic differential operators in case of mixed boundary conditions
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Lp regularity for abstract differential equations
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Hölder Continuity and Optimal Control for Nonsmooth Elliptic Problems
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Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semilinear Elliptic Equations
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W1,p-estimates of solutions to evolution equations corresponding to nonsmooth second order elliptic differential operators
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The Finite Element Method for Elliptic Problems
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Boundary Control of Semilinear Elliptic Equations with Pointwise State Constraints
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Feasible and Noninterior Path‐Following in Constrained Minimization with Low Multiplier Regularity
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Optimal Control of a Convective Boundary Condition in a Thermistor Problem
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Sufficient Second-Order Optimality Conditions for Semilinear Control Problems with Pointwise State Constraints
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Elliptic Problems in Nonsmooth Domains
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The Thermistor Problem: Existence, Smoothness Uniqueness, Blowup
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Analysis of Optimal Control Problems for the Two-Dimensional Thermistor System
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An Extension of Pontryagin’s Principle for State-Constrained Optimal Control of Semilinear Elliptic Equations and Variational Inequalities
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Second Order Sufficient Optimality Conditions for Some State-constrained Control Problems of Semilinear Elliptic Equations
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NUMERICAL MODELING OF INDUCTION HEATING FOR TWO-DIMENSIONAL GEOMETRIES
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Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen
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Second order sufficient optimality conditions for nonlinear parabolic control problems with state constraints
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Maximum principle for state-constrained optimal control problems governed by quasilinear elliptic

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