Nonlinear potential theoretic methods in nonuniformly ellliptic problems

2024/02/05 by Giuseppe Mingione, Mingione, Giuseppe · 2 citations
Computer Science · Engineering · Mathematics · #31C45 #35J60 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2402.02683

openalex publication_date 2024/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Nonuniform ellipticity is a classical topic in the theory of partial differential equations. While several results in regularity theory have been adding up over decades, many basic issues, as for instance the validity of Schauder theory and sharp dependence of regularity upon data, remained opened for a while. In these notes we give an overview of recent results and techniques about the topic, that, via a novel use of nonlinear potential theoretic methods, allow to answer several of the above questions.

Cited by

• Regularity for quasilinear elliptic equations in metric measure spaces
• Higher Hölder regularity for degenerate elliptic PDEs with data in Morrey spaces

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