Examples of optimal Hölder regularity in semilinear equations involving the fractional Laplacian
We discuss the Hölder regularity of solutions to the semilinear equation involving the fractional Laplacian (−Δ)su=f(u) in one dimension. We put in evidence a new regularity phenomenon which is a combined effect of the nonlocality and the semilinearity of the equation, since it does not happen neith...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/484442 |
| Acceso en línea: | http://hdl.handle.net/2072/484442 |
| Access Level: | acceso abierto |
| Palabra clave: | Fractional Laplacian Hölder regularity Semilinear equations 51 |
| Sumario: | We discuss the Hölder regularity of solutions to the semilinear equation involving the fractional Laplacian (−Δ)su=f(u) in one dimension. We put in evidence a new regularity phenomenon which is a combined effect of the nonlocality and the semilinearity of the equation, since it does not happen neither for local semilinear equations, nor for nonlocal linear equations. Namely, for nonlinearities f in Cβ and when 2s+β<1, the solution is not always C2s+β−ϵ for all ϵ>0. Instead, in general the solution u is at most C2s/(1−β). |
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