On the Convergence of a Class of Nonlocal Elliptic Equations and Related Optimal Design Problems

被引：14

作者：

Andres, Fuensanta ^{[1
]}

Munoz, Julio ^{[1
]}

机构：

[1] Univ Castilla La Mancha, Toledo, Spain

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2017年 / 172卷 / 01期

关键词：

Approximation of partial differential equations; Optimal control; Integral equations; G-convergence; VECTOR CALCULUS; APPROXIMATION; EXISTENCE; LIMIT;

D O I：

10.1007/s10957-016-1021-z

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

A convergence result for a nonlocal differential equation problem is proved. As a by-product, some results about the convergence for a type of nonlocal optimal design are given. Since these problems give rise to local design problems in the limit, different results on classical existence are obtained as well. Concerning the nonlocal formulation, the state equation is of nonlocal elliptic type and the cost functional we analyze includes, among other cases, an approximation of the square of the gradient.

引用

页码：33 / 55

页数：23

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