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...
| Authors: | , |
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| 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 51 |
| 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. |
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