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

Liu, Yichen and Emamizadeh, Behrouz and Farjudian, Amin (2016) Optimization problems with fixed volume constraints and stability results related to rearrangement classes. Journal of Mathematical Analysis and Applications, 443 (2). pp. 1293-1310. ISSN 0022-247X

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Abstract

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 ob- tained 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 do- mains. 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.

Item Type: Article
Keywords: Trace inequality, Boundary value problem, Maximization, Mini- mization, Approximation, Stability, Rearrangement theory
Schools/Departments: University of Nottingham Ningbo China > Faculty of Science and Engineering > School of Mathematical Sciences
Identification Number: https://doi.org/10.1016/j.jmaa.2016.06.017
Depositing User: LI, Zhilin
Date Deposited: 06 Apr 2018 11:11
Last Modified: 15 Nov 2018 04:30
URI: http://eprints.nottingham.ac.uk/id/eprint/50886

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