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

TL;DR

This paper revisits foundational results in nonlinear potential theory related to the p-Laplacian, offering simplified proofs and improvements on classical findings about boundary points and boundary value problems.

Contribution

It provides new, simpler proofs of early 1970s results in nonlinear potential theory for the p-Laplacian and enhances some existing theorems in the literature.

Findings

Simplified proofs of classical results from the 1970s

Improved theorems regarding boundary points for the p-Laplacian

Enhanced understanding of nonlinear potential theory in N 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-Laplacian 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.