Global Hölder solvability of linear and quasilinear Poisson equations

2023/11/16 by Takanobu Hara, Hara, Takanobu
Computer Science · Mathematics · #31C45 #35J25 #35J92 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2311.09701

openalex publication_date 2023/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish an existence result for globally continuous weak solutions to elliptic equations of the p-Poisson type. This result significantly improves Theorem 8.30 in Gilbarg-Trudinger (1983) and offers a novel contribution for the classical Poisson equation on Lipschitz domains, ensuring global Hölder continuity of solutions under a minimal assumption on the right-hand side. Applications of this result to embedding theorems are also discussed.

Related

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