Hölder regularity of stable solutions to elliptic equations up to R9: Full quantitative proofs
This article concerns the results obtained in [Cabré, Figalli, Ros-Oton, and Serra, Acta Math. 224 (2020)], which established the Hölder regularity of stable solutions to semilinear elliptic equations in the optimal range of dimensions n <= 9. For expository purposes, we provide self-contained pr...
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| Formato: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:dnet:upcommonspor::4ec885947a3a9b4f050ef6791f365a73 |
| Acesso em linha: | https://hdl.handle.net/2117/462458 https://dx.doi.org/10.1090/bull/1873 |
| Access Level: | acceso abierto |
| Palavra-chave: | Partial differential equations Elliptic equations Elliptic systems Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials |
| Resumo: | This article concerns the results obtained in [Cabré, Figalli, Ros-Oton, and Serra, Acta Math. 224 (2020)], which established the Hölder regularity of stable solutions to semilinear elliptic equations in the optimal range of dimensions n <= 9. For expository purposes, we provide self-contained proofs of all results. They involve only basic analysis tools and are intended to be accessible to a broader mathematical audience beyond PDE specialists. Two of the results in the 2020 article relied on compactness arguments. Here we present, instead, quantitative proofs from the more recent paper [Cabré, to appear in Amer. J. Math, arXiv:2211.13033]. They allow us to quantify the Hölder regularity exponent and significantly simplify the treatment of boundary regularity. We also comment on similar progress and open problems for related equations. |
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