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

Sun-Sig Byun; Hongsoo Kim

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arXiv · 2505.15119

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

Sun-Sig Byun·Hongsoo Kim

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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 H\"older 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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Sun-Sig Byun, Hongsoo Kim. 2025-05-21. Lipschitz regularity for fully nonlinear elliptic equations with $(p,q)$-growth. https://arxiv.org/abs/2505.15119

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