Regularity theory for degenerate fully nonlinear nonlocal equations with a Hamiltonian term

Yuzhou Fang; Juha Kinnunen; Chao Zhang

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arXiv · 2511.13403

Regularity theory for degenerate fully nonlinear nonlocal equations with a Hamiltonian term

Yuzhou Fang·Juha Kinnunen·Chao Zhang

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Abstract

We investigate a class of degenerate fully nonlinear nonlocal elliptic equations with Hamiltonian terms. By precisely characterizing the interaction between the degeneracy law of equations and the growth behavior of the Hamiltonian terms, we establish the Lipschitz regularity of viscosity solutions by the Ishii-Lions method, and further show the gradient H\"{o}lder continuity for solutions via utilizing perturbation techniques. Additionally, under minimal assumptions on the degeneracy pattern, the $C^1$-differentiability property of solutions is explored as well.

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Yuzhou Fang, Juha Kinnunen, Chao Zhang. 2025-11-17. Regularity theory for degenerate fully nonlinear nonlocal equations with a Hamiltonian term. https://arxiv.org/abs/2511.13403

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