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Optimization problems with fixed volume constraints and stability results related to rearrangement classes
Beijing International Center for Mathematical Research, Peking University, China.
School of Mathematical Sciences, The University of Nottingham-Ningbo, China.
Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES).ORCID iD: 0000-0002-1879-0763
2016 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 443, no 2, 1293-1310 p.Article in journal (Refereed) Published
Abstract [en]

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. © 2016 Elsevier 

Place, publisher, year, edition, pages
Oxford: Elsevier, 2016. Vol. 443, no 2, 1293-1310 p.
Keyword [en]
Trace inequality, Boundary value problem, Optimization, Approximation, Stability, Rearrangement theory
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:hh:diva-31359DOI: 10.1016/j.jmaa.2016.06.017OAI: oai:DiVA.org:hh-31359DiVA: diva2:942027
Available from: 2016-06-23 Created: 2016-06-23 Last updated: 2016-06-29Bibliographically approved

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Farjudian, Amin
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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
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  • nn-NO
  • nn-NB
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  • Other locale
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