Nonstandard growth optimization problems with volume constraint

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-07-28 DOI:10.57262/die036-0708-573

A. Salort, Belem Schvager, Analía Silva

引用次数: 1

Abstract

In this article we study some optimal design problems related to nonstandard growth eigenvalues ruled by the $g-$Laplacian operator. More precisely, given $\Omega\subset \R^n$ and $\alpha,c>0$ we consider the optimization problem $\inf \{ \lambda_\Omega(\alpha,E)\colon E\subset \Omega, |E|=c \}$, where $\lambda_\Omega(\alpha,E)$ is related to the first eigenvalue to $$ -\text{div}(g( |\nabla u |)\tfrac{\nabla u}{|\nabla u|}) + g(u)\tfrac{u}{|u|}+ \alpha \chi_E g(u)\tfrac{u}{|u|} \quad \text{ in }\Omega $$ subject to Dirichlet, Neumann or Steklov boundary conditions. \\ We analyze existence of an optimal configuration, symmetry properties of them, and the asymptotic behavior as $\alpha$ approaches $+\infty$.

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体积约束下的非标准生长优化问题

本文研究了一些由$g-$拉普拉斯算子控制的非标准生长特征值的优化设计问题。更准确地说，给定$\Omega\subset \R^n$和$\alpha,c>0$，我们考虑优化问题$\inf \{ \lambda_\Omega(\alpha,E)\colon E\subset \Omega, |E|=c \}$，其中$\lambda_\Omega(\alpha,E)$与Dirichlet, Neumann或Steklov边界条件下$$ -\text{div}(g( |\nabla u |)\tfrac{\nabla u}{|\nabla u|}) + g(u)\tfrac{u}{|u|}+ \alpha \chi_E g(u)\tfrac{u}{|u|} \quad \text{ in }\Omega $$的第一个特征值相关。 \\ 我们分析了最优构型的存在性，它们的对称性，以及当$\alpha$逼近$+\infty$时的渐近性。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.