Concentration breaking on two optimization problems

作     者：Yong Huang Qinfeng Li Qiuqi Li 

作者机构：School of MathematicsHunan UniversityChangsha410082China 

出 版 物：《Science China Mathematics》 (中国科学（数学）（英文版）)

年 卷 期：2024年第67卷第7期

页      面：1555-1570页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11625103 and 12171144) Hunan Science and Technology Planning Project (Grant No. 2019RS3016) supported by the National Natural Science Fund for Youth Scholars (Grant No. 12101215) Scientific Research Start-Up Funds by Hunan University supported by the National Natural Science Fund for Youth Scholars (Grant No. 12101216 ) the Natural Science Fund of Hunan Province (Grant No. 2022JJ40030) 

主　　题：spectral inequalities symmetry breaking Laplacian eigenvalue 

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 C^(1), another key ingredient is to obtain the global H?lder 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.