Schauder and Cordes–Nirenberg estimates for nonlocal elliptic equations with singular kernels
Abstract We study integro‐differential elliptic equations (of order ) 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 Hölder estimates for general elliptic equations with no regularity assumption on , including for the first‐time operators like , provided that the coefficients have “small oscillation.”
Authors
- Xavier Ros‐Oton (ORCID: https://orcid.org/0000-0003-1046-168X)
- Xavier Fernández‐Real (ORCID: https://orcid.org/0000-0002-6775-315X)
Institutions
- Institució Catalana de Recerca i Estudis Avançats (ES)
- Centre de Recerca Matemàtica (ES)
- École Polytechnique Fédérale de Lausanne (CH)
- Universitat de Barcelona (ES)
Publication Details
- Journal
- Proceedings of the London Mathematical Society
- Published
- 2024-08-20
- DOI
- https://doi.org/10.1112/plms.12629
- Citations
- 4
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 1.45
Funders
- Scientific Education and Research Institute
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- European Research Council
- Agència de Gestió d'Ajuts Universitaris i de Recerca
- Agencia Estatal de Investigación