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

Liu, Yichen; Emamizadeh, Behrouz; Farjudian, Amin

Authors

Yichen Liu

Behrouz Emamizadeh Behrouz.Emamizadeh@nottingham.edu.cn

Amin Farjudian



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.

Journal Article Type Article
Publication Date Nov 15, 2016
Journal Journal of Mathematical Analysis and Applications
Print ISSN 0022-247X
Electronic ISSN 0022-247X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 443
Issue 2
APA6 Citation Liu, Y., Emamizadeh, B., & Farjudian, A. (2016). Optimization problems with fixed volume constraints and stability results related to rearrangement classes. Journal of Mathematical Analysis and Applications, 443(2), https://doi.org/10.1016/j.jmaa.2016.06.017
DOI https://doi.org/10.1016/j.jmaa.2016.06.017
Keywords Trace inequality, Boundary value problem, Maximization, Mini- mization, Approximation, Stability, Rearrangement theory
Publisher URL https://www.sciencedirect.com/science/article/pii/S0022247X16302475?via%3Dihub
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf



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