Work

Lipschitz regularity for fully nonlinear elliptic equations with $(p,q)$-growth

Year: 2025

Type: preprint

Abstract: We prove the interior and global Lipschitz regularity results for a solution of fully nonlinear equations with $(p,q)$-growth. We prove that for a small gap $q-p$, a solution is locally or globally Lipschitz continuous. We also prove that a given Hölder continuous solution is Lipschitz continuous under improved bounds for the gap. These gap conditions are similar to those required for the regularity of double phase problems in divergence form.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2505.15119

Authors: Byun, Sun-Sig, Kim, Hongsoo

Institution: Seoul National University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Research Foundation, Seoul National University, National Research Foundation of Korea

Award: G397763134

OpenAlex ID: W4415328524

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