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arXiv · 2408.15559

Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations

Yuzhou Fang·Vicentiu D. Radulescu·Chao Zhang
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Abstract

We consider a wide class of fully nonlinear integro-differential equations that degenerate when the gradient of the solution vanishes. By using compactness and perturbation arguments, we give a complete characterization of the regularity of viscosity solutions according to different diffusion orders. More precisely, when the order of the fractional diffusion is sufficiently close to 2, we obtain H\"{o}lder continuity for the gradient of any viscosity solutions and further derive an improved gradient regularity estimate at the origin. For the order of the fractional diffusion in the interval $(1, 2)$, we prove that there is at least one solution of class $C^{1, \alpha}_{\rm loc}$. Additionally, if the order of the fractional diffusion is in the interval $(0,1]$, the local H\"{o}lder continuity of solutions is inferred.

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Yuzhou Fang, Vicentiu D. Radulescu, Chao Zhang. 2024-08-28. Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations. https://arxiv.org/abs/2408.15559

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