Shape optimization problems in control form

IF 0.6 4区 数学 Q3 MATHEMATICS
G. Buttazzo, Francesco Paolo Maiale, B. Velichkov
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引用次数: 4

Abstract

We consider a shape optimization problem written in the optimal control form: the governing operator is the p-Laplacian in the Euclidean space R, the cost is of an integral type, and the control variable is the domain of the state equation. Conditions that guarantee the existence of an optimal domain will be discussed in various situations. It is proved that the optimal domains have a finite perimeter and, under some suitable assumptions, that they are open sets. A crucial difference is between the case p > d, where the existence occurs under very mild conditions, and the case p ≤ d, where additional assumptions have to be made on the data.
控制形式下的形状优化问题
考虑一个以最优控制形式表示的形状优化问题:控制算子为欧几里德空间R中的p-拉普拉斯算子,代价为积分型,控制变量为状态方程的定域。保证最优域存在的条件将在各种情况下进行讨论。证明了最优域的周长是有限的,并且在适当的假设下,它们是开集。一个关键的区别在于p > d的情况,即在非常温和的条件下存在,而p≤d的情况,则必须对数据做出额外的假设。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Rendiconti Lincei-Matematica e Applicazioni
Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.30
自引率
0.00%
发文量
27
审稿时长
>12 weeks
期刊介绍: The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.
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