Rearrangements and minimization of the principal eigenvalue of a nonlinear Steklov problem

Behrouz Emamizadeh, Mohsen Zivari-Rezapour

Research output: Journal PublicationArticlepeer-review

9 Citations (Scopus)

Abstract

This paper, motivated by Del Pezzo et al. (2006) [1], discusses the minimization of the principal eigenvalue of a nonlinear boundary value problem. In the literature, this type of problem is called Steklov eigenvalue problem. The minimization is implemented with respect to a weight function. The admissible set is a class of rearrangements generated by a bounded function. We merely assume the generator is non-negative in contrast to [1], where the authors consider weights which are positively away from zero, in addition to being two-valued. Under this generality, more physical situations can be modeled. Finally, using rearrangement theory developed by Geoffrey Burton, we are able to prove uniqueness of the optimal solution when the domain of interest is a ball.

Original languageEnglish
Pages (from-to)5697-5704
Number of pages8
JournalNonlinear Analysis, Theory, Methods and Applications
Volume74
Issue number16
DOIs
Publication statusPublished - Nov 2011
Externally publishedYes

Keywords

  • Existence
  • Minimization
  • Principal eigenvalue
  • Rearrangement theory
  • Steklov eigenvalue problem
  • Uniqueness

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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