Optimization of the first eigenvalue in problems involving the p-Laplacian

Fabrizio Cuccu, Behrouz Emamizadeh, Giovanni Porru

Research output: Journal PublicationArticlepeer-review

38 Citations (Scopus)

Abstract

This paper concerns minimization and maximization of the first eigenvalue in problems involving the p-Laplacian, under homogeneous Dirichlet boundary conditions. Physically, in the case of N = 2 and p close to 2, our equation models the vibration of a nonhomogeneous membrane Ω which is fixed along the boundary. Given several materials (with different densities) of total extension |Ω|, we investigate the location of these material inside Ω so as to minimize or maximize the first mode in the vibration of the membrane.

Original languageEnglish
Pages (from-to)1677-1687
Number of pages11
JournalProceedings of the American Mathematical Society
Volume137
Issue number5
DOIs
Publication statusPublished - May 2009
Externally publishedYes

Keywords

  • Eigenvalues
  • P-Laplacian
  • Rearrangements
  • Shape optimization

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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