An extension problem for sums of fractional Laplacians and 1-D symmetry of phase transitions
We study nonlinear elliptic equations for operators corresponding to non-stable Lévy diffusions. We include a sum of fractional Laplacians of different orders. Such operators are infinitesimal generators of non-stable (i.e., non self-similar) Lévy processes. We establish the regularity of solutions,...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/85537 |
| Acceso en línea: | https://hdl.handle.net/2117/85537 https://dx.doi.org/10.1016/j.na.2015.12.014 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential equations, Elliptic Conjecture of De Giorgi One-dimensional symmetry Sums of fractional Laplacians Equacions diferencials el·líptiques Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | We study nonlinear elliptic equations for operators corresponding to non-stable Lévy diffusions. We include a sum of fractional Laplacians of different orders. Such operators are infinitesimal generators of non-stable (i.e., non self-similar) Lévy processes. We establish the regularity of solutions, as well as sharp energy estimates. As a consequence, we prove a 1-D symmetry result for monotone solutions to Allen-Cahn type equations with a non-stable Lévy diffusion. These operators may still be realized as local operators using a system of PDEs - in the spirit of the extension problem of Caffarelli and Silvestre. |
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