Regularity of multipliers and second-order optimality conditions of KKT-type for semilinear parabolic control problems

Abstract

A class of optimal control problems governed by semilinear parabolic equations with mixed constraints and a box constraint for control variable is considered. We show that if the separation condition is satisfied, then both optimality conditions of KKT-type and regularity of multipliers are fulfilled. Moreover, we show that if the initial value is good enough and boundary $\partial \Omega$ has a property of positive geometric density, then multipliers and optimal solutions are Hölder continuous.

arXiv admin note: substantial text overlap with arXiv:2306.10295