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...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2011 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:76163 |
| Online Access: | https://ddd.uab.cat/record/76163 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_55211_08 |
| Access Level: | Open access |
| Keyword: | Boundary value problems Nonlinear elliptic equations Hausdorff distance Reifenberg-flat sets Mosco convergence |
| Summary: | 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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