On nonlinear potential theory, and regular boundary points, for the p-Laplacian in N space variables

Abstract

We turn back to some pioneering results concerning, in particular, nonlinear potential theory and non-homogeneous boundary value problems for the so-called p-Laplace operator. Unfortunately these results, obtained at the very beginning of the seventies, were kept in the shade. We believe that our proofs are still of interest, in particular due to their extreme simplicity. Moreover, some contributions seem to improve the results quoted in the current literature.

Keywords

• p-laplacian
• non-homogeneous dirichlet problem
• barriers
• capacitary potentials
• regular boundary points
• 35j62
• 35j92
• 31c05
• 31c15
• 31c45