Non-homogeneous Dirichlet boundary value problems in weighted Sobolev spaces

V. Gol’dshtein, D. Motreanu, V. V. Motreanu

Research output: Contribution to journalArticlepeer-review

Abstract

The paper presents existence and multiplicity results for non-linear boundary value problems on possibly non-smooth and unbounded domains under possibly non-homogeneous Dirichlet boundary conditions. We develop here an appropriate functional setting based on weighted Sobolev spaces. Our results are obtained by using global minimization and a minimax approach using a non-smooth critical point theory.

Original languageEnglish
Pages (from-to)372-391
Number of pages20
JournalComplex Variables and Elliptic Equations
Volume60
Issue number3
DOIs
StatePublished - 4 Mar 2015

Keywords

  • global optimization
  • minimax principle
  • non-homogeneous Dirichlet boundary conditions
  • non-linear elliptic problem
  • weighted Sobolev spaces

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