On the pure critical exponent problem for the $p$-Laplacian

Carlo Mercuri; Filomena Pacella

On the pure critical exponent problem for the $p$-Laplacian

Analysis of PDEs 2013-01-23 v2

Authors: Carlo Mercuri , Filomena Pacella

Abstract

In this paper we prove existence and multiplicity of positive and sign-changing solutions to the pure critical exponent problem for the $p$ -Laplacian operator with Dirichlet boundary conditions on a bounded domain having nontrivial topology and discrete symmetry. Pioneering works related to the case $p=2$ are H. Brezis and L. Nirenberg [4], J.-M. Coron [10], and A. Bahri and J.-M. Coron [3]. A global compactness analysis is given for the Palais-Smale sequences in the presence of symmetries.

Keywords

p-Laplacian critical exponent positive solutions sign-changing solutions Dirichlet boundary conditions nontrivial topology discrete symmetry Palais-Smale sequences

Cite

@article{arxiv.1206.4341,
  title  = {On the pure critical exponent problem for the $p$-Laplacian},
  author = {Carlo Mercuri and Filomena Pacella},
  journal= {arXiv preprint arXiv:1206.4341},
  year   = {2013}
}

Comments

18 pages

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