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This is a Quantitative Study study.

October 20, 2025Open Access

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

Key Points

A solution to fully nonlinear equations shown to be Lipschitz continuous under certain conditions.
For small gap conditions, both local and global Lipschitz regularity is established.
Hölder continuous solutions can become Lipschitz continuous with improved growth bounds.
The gap conditions align with those used in regularity for double phase problems.

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.

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Cite This Study

Byun et al. (Wed,) studied this question.

synapsesocial.com/papers/68f5c338e2d8b128426459ca https://doi.org/https://doi.org/10.48550/arxiv.2505.15119

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