Optimization problems with fixed volume constraints and stability results related to rearrangement classes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:443

Article

Liu, Yichen¹  Emamizadeh, Behrouz²  Farjudian, Amin³ 

[1] Peking Univ, Beijing Int Ctr Math Res, Beijing, Peoples R China

[2] Univ Nottingham Ningbo, Sch Math Sci, Ningbo, Zhejiang, Peoples R China

[3] Halmstad Univ, Ctr Res Embedded Syst, Halmstad, Sweden

关键词: Trace inequality;    Boundary value problem;    Optimization;    Approximation;    Stability;    Rearrangement theory;   

DOI  :  10.1016/j.jmaa.2016.06.017

来源: Elsevier

【 摘 要 】

The material in this paper has been divided into two main parts. In the first part we describe two optimization problems-one maximization and one minimization related to a sharp trace inequality that was recently obtained by G. Auchmuty. In both problems the admissible set is the one comprising characteristic functions whose supports have a fixed measure. We prove the maximization to be solvable, whilst the minimization will turn out not to be solvable in general. We will also discuss the case of radial domains. In the second part of the paper, we study approximation and stability results regarding rearrangement optimization problems. First, we show that if a sequence of the generators of rearrangement classes converges, then the corresponding sequence of the optimal solutions will also converge. Second, a stability result regarding the Hausdorff distance between the weak closures of two rearrangement classes is presented. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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