Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift

Barbara Brandolini, Barbara Brandolini, Francesco Chiacchio, Cristina Trombetti, Antoine Henrot

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2 Citations (Scopus)

Abstract

This paper deals with the eigenvalue problem for the operator L=-δ-x{dot operator}∇ with Dirichlet boundary conditions. We are interested in proving the existence of a set minimizing any eigenvalue λk of L under a suitable measure constraint suggested by the structure of the operator. More precisely we prove that for any c>0 and k∈N the following minimization problemmin<>{λk(Ω):Ωquasi-openset,∫Ωe|x|2/2dx≤c} has a solution.
Original languageEnglish
Pages (from-to)708-727
Number of pages20
JournalJournal of Differential Equations
Volume259
Publication statusPublished - 2015

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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