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arXiv · 2308.11383

Schauder and Cordes-Nirenberg estimates for nonlocal elliptic equations with singular kernels

Xavier Fernández-Real·Xavier Ros-Oton
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Abstract

We study integro-differential elliptic equations (of order $2s$) with variable coefficients, and prove the natural and most general Schauder-type estimates that can hold in this setting, both in divergence and non-divergence form. Furthermore, we also establish H\"older estimates for general elliptic equations with no regularity assumption on $x$, including for the first time operators like $\sum_{i=1}^n(-\partial^2_{\textbf{v}_i(x)})^s$, provided that the coefficients have ``small oscillation''.

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Xavier Fernández-Real, Xavier Ros-Oton. 2023-08-22. Schauder and Cordes-Nirenberg estimates for nonlocal elliptic equations with singular kernels. https://arxiv.org/abs/2308.11383

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