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

We study integro-differential elliptic equations (of order 2s$2s$) 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 & ouml;lder estimates for gene...

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Bibliographic Details
Authors: Fernández-Real, X., Ros-Oton, X.
Format: article
Publication Date:2024
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/479529
Online Access:http://hdl.handle.net/2072/479529
Access Level:Open access
Keyword:Integro-differential operators
Smoothness and regularity of solutions to PDEs
Fractional partial differential equations
Stable stochastic processes
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Description
Summary:We study integro-differential elliptic equations (of order 2s$2s$) 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 & ouml;lder estimates for general elliptic equations with no regularity assumption on x$x$, including for the first-time operators like & sum;i=1n(-partial derivative vi(x)2)s$\sum _{i=1}<^>n(-\partial <^>2_{{\bf v}_i(x)})<^>s$, provided that the coefficients have small oscillation.