Concentration breaking on two optimization problems

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外文摘要：In the present paper,we study the boundary concentration-breaking phenomena on two thermal insulation problems considered on Lipschitz domains,based on Serrin's overdetermined result,the perturbation argument,and a comparison of Laplacian eigenvalues with different boundary conditions.Since neither of the functionals in the two problems is C1,another key ingredient is to obtain the global Hölder regularity of minimizers of both problems on Lipschitz domains.Also,the exact dependence on the domain of breaking thresholds is given in the first problem,and the breaking values are obtained in the second problem on ball domains,which are related to 2π in dimension 2.

外文关键词：

spectral inequalitiessymmetry breakingLaplacian eigenvalue

作者：

Yong Huang、Qinfeng Li、Qiuqi Li

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作者单位：

School of Mathematics,Hunan University,Changsha 410082,China

基金：

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaHunan Science and Technology Planning ProjectNational Natural Science Fund for Youth ScholarsScientific Research Start-Up Funds by Hunan UniversityNational Natural Science Fund for Youth ScholarsNatural Science Fund of Hunan Province

项目编号：

11625103121711442019RS301612101215121012162022JJ40030

出版年：

2024

DOI：

10.1007/s11425-022-2128-5

中国科学:数学(英文版)

中国科学院

中国科学:数学(英文版)

CSTPCD

影响因子：0.36

ISSN：1674-7283

年,卷(期)：2024.67(7)