Embeddings of weighted Sobolev spaces and degenerate dirichlet problems involving the weighted P-Laplacian

V. Gol'dshtein, V. V. Motreanu, A. Ukhlov

Research output: Contribution to journalArticlepeer-review

Abstract

We deal with two Dirichlet boundary value problems involving the weighted p-Laplacian. We introduce double weighted Sobolev spaces as solution spaces of the considered problems. We show the existence of weak solutions of these problems under an assumption of compact embedding involving the double weighted Sobolev spaces. Also, we establish sufficient conditions for fulfilling this embedding assumption.

Original languageAmerican English
Pages (from-to)905-930
Number of pages26
JournalComplex Variables and Elliptic Equations
Volume56
Issue number10-11
DOIs
StatePublished - 1 Oct 2011

Keywords

  • Dirichlet problems
  • Dirichlet spaces
  • Embedding properties
  • P-laplacian
  • Quasiconformal mappings
  • Weighted sobolev spaces

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Embeddings of weighted Sobolev spaces and degenerate dirichlet problems involving the weighted P-Laplacian'. Together they form a unique fingerprint.

Cite this