Optimal Lipschitz criteria and local estimates for non-uniformly elliptic problems

DOI10.4171/RLM/844zbMATH Open1471.49024arXiv1806.03326OpenAlexW2963606138WikidataQ127645986 ScholiaQ127645986MaRDI QIDQ2319582

Lisa Beck, Giuseppe Mingione

Publication date: 20 August 2019

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Abstract: We report on new techniques and results in the regularity theory of general non-uniformly elliptic variational integrals. By means of a new potential theoretic approach we reproduce, in the non-uniformly elliptic setting, the optimal criteria for Lipschitz continuity known in the uniformly elliptic one and provide a unified approach between non-uniformly and uniformly elliptic problems.

Full work available at URL: https://arxiv.org/abs/1806.03326

zbMATH Keywords

regularityLorentz spacesnon-uniform ellipticity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate elliptic equations (35J70) Regularity of solutions in optimal control (49N60)

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