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arXiv · 2212.07228

Cordes-Nirenberg type results for nonlocal equations with deforming kernels

Disson dos Prazeres·Aelson Sobral·José Miguel Urbano
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Abstract

We derive Cordes-Nirenberg type results for nonlocal elliptic integro-differential equations with deforming kernels comparable to sections of a convex solution of a Monge-Amp\`ere equation. Under a natural integrability assumption on the Monge-Amp\`ere solution, we prove a stability lemma allowing the ellipticity class to vary. Using a compactness method, we then derive H\"older regularity estimates for the gradient of the solutions.

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Disson dos Prazeres, Aelson Sobral, José Miguel Urbano. 2022-12-14. Cordes-Nirenberg type results for nonlocal equations with deforming kernels. https://arxiv.org/abs/2212.07228

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