Analysis of control problems of nonmontone semilinear elliptic equations

Abstract

In this paper we study optimal control problems governed by a semilinear elliptic equation. The equation is nonmonotone due to the presence of a convection term, despite the monotonocity of the nonlinear term. The resulting operator is neither monotone nor coervive. However, by using conveniently a comparison principle we prove existence and uniqueness of solution for the state equation. In addition, we prove some regularity of the solution and differentiability of the relation control-to-state. This allows us to derive first and second order conditions for local optimality.

arXiv comment20 pages; In this version, we correct the end of Step 1 of the proof of Theorem 2.2 as well as some typos

References in corpus (2)

• Inverse Problem for a Curved Quantum Guide
• Critical cones for sufficient second order conditions in PDE constrained optimization

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