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

Published 22 Aug 2023 in math.AP | (2308.11383v1)

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 $\sum_{i=1}n(-\partial2_{\textbf{v}_i(x)})s$, provided that the coefficients have ``small oscillation''.

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