OPTIMAL-CONTROL OF SEMILINEAR ELLIPTIC-EQUATIONS WITH POINTWISE CONSTRAINTS ON THE GRADIENT OF THE STATE

被引：31

作者：

CASAS, E ^{[1
]}

FERNANDEZ, LA ^{[1
]}

机构：

[1] UNIV CANTABRIA,FAC CIENCIAS,DEPT MATEMAT,E-39071 SANTANDER,SPAIN

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 1993年 / 27卷 / 01期

关键词：

OPTIMAL CONTROL; STATE CONSTRAINTS; SEMILINEAR ELLIPTIC EQUATIONS; OPTIMALITY CONDITIONS; LAGRANGE MULTIPLIERS;

D O I：

10.1007/BF01182597

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we are concerned with optimal control problems governed by an elliptic semilinear equation, the control being distributed in OMEGA. The existence of constraints on the control as well as pointwise constraints on the gradient of the state is assumed. A convenient choice of the control space permits us to derive the optimality conditions and study the adjoint state equation, which has derivatives of measures as data. In order to carry out this study, we prove a trace theorem and state Green's formula by using the transposition method.

引用

页码：35 / 56

页数：22

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