State-constrained relaxed problems for semilinear elliptic equations

被引：10

作者：

Arada, N ^{[1
]}

Raymond, JP ^{[1
]}

机构：

[1] Univ Toulouse 3, CNRS, UMR, MIP, F-31062 Toulouse, France

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1998年 / 223卷 / 01期

关键词：

optimal control; relaxed solutions; Young measures; Pontryagin's minimum principle; pointwise state constraints;

D O I：

10.1006/jmaa.1998.5976

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study optimal control problems governed by semilinear elliptic equations in the presence of pointwise state constraints. Since no convexity condition is assumed on data of the problem, we define a relaxed control problem, prove the existence of relaxed solutions, and give some relaxation results. By adapting the penalty method of Berkovitz, we prove a Pontryagin's minimum principle for relaxed solutions in nonqualified form and in qualified form under a stability condition. (C) 1998 Academic Press.

引用

页码：248 / 271

页数：24

共 25 条

[1] Boundary control of semilinear elliptic equations with discontinuous leading coefficients and unbounded controls [J].