A stability result for nonlinear neumann problems in reifenberg flat domains in Rn
In this paper we prove that if Ωk is a sequence of Reifenberg-flat domains in RN that converges to Ω for the complementary Hausdorff distance and if in addition the sequence Ωk has a "uniform size of holes", then the solutions uk of a Neumann problem of the form (...) converge to the soluti...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:76163 |
| Acceso en línea: | https://ddd.uab.cat/record/76163 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_55211_08 |
| Access Level: | acceso abierto |
| Palabra clave: | Boundary value problems Nonlinear elliptic equations Hausdorff distance Reifenberg-flat sets Mosco convergence |
| Sumario: | In this paper we prove that if Ωk is a sequence of Reifenberg-flat domains in RN that converges to Ω for the complementary Hausdorff distance and if in addition the sequence Ωk has a "uniform size of holes", then the solutions uk of a Neumann problem of the form (...) converge to the solution u of the same Neumann problem in Ω. The result is obtained by proving the Mosco convergence of some Sobolev spaces, that follows from the extension property of Reifenberg-flat domains. |
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