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

2013/04/04 by H. Beirão da Veiga, H. Beirao da Veiga, da Veiga, H. Beirao
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1304.1312

arxiv created 2013/04/04 · openalex publication_date 2013/04/04 · arxiv updated 2013/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• C1 + α local regularity of weak solutions of degenerate elliptic equations

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