On Regularity of Solutions and Lagrange Multipliers of Optimal Control Problems for Semilinear Equations with Mixed Pointwise Control-State Constraints

Authors:
A. Rösch;F. Tröltzsch
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2007

Citing 0
Cited 6

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A Priori Error Analysis for Linear Quadratic Elliptic Neumann Boundary Control Problems with Control and State Constraints

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Stability of semilinear elliptic optimal control problems with pointwise state constraints

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Regularization for semilinear elliptic optimal control problems with pointwise state and control constraints

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Abstract

A class of nonlinear elliptic and parabolic optimal control problems with mixed control-state constraints is considered. Extending a method known for the control of ordinary differential equations to the case of PDEs, the Yosida-Hewitt theorem is applied to show that the Lagrange multipliers are functions of certain $L^p$-spaces. By bootstrapping arguments, under natural assumptions, optimal controls are shown to be Lipschitz continuous in the elliptic case and Hölder continuous for parabolic problems.