Embedding operators and boundary-value problems for rough domains

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dc.creatorGoldshtein, V. G.
dc.creatorRamm, A. G.
dc.date2004-11-08
dc.date.accessioned2026-07-07T05:14:06Z
dc.date.available2026-07-07T05:14:06Z
dc.descriptionIn the first part of the paper boundary-value problems are considered under weak assumptions on the smoothness of the domains. We assume nothing about smoothness of the boundary $\partial D$ of a bounded domain $D$ when the homogeneous Dirichlet boundary condition is imposed; we assume boundedness of the embedding $i_{1}:H^{1}(D)\to L^{2}(D)$ when the Neumann boundary condition is imposed; we assume boundedness of the embeddings $i_{1}$ and of $i_{2}:H^{1}(D)\to L^{2}(\partial D)$ when the Robin boundary condition is imposed, and, if, in addition, $i_{1}$ and $i_{2}$ are compact, then the boundary-value problems with the spectral parameter are of Fredholm type. Several examples of the classes of rough domains for which the embedding $i_2$ is compact are given. Applications to scattering by rough obstacles are mentioned.
dc.identifierhttps://arxiv.org/abs/math/0411176
dc.identifierhttp://arxiv.org/abs/math/0411176
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73149
dc.subjectAnalysis of PDEs
dc.subject35R30
dc.titleEmbedding operators and boundary-value problems for rough domains
dc.typetext

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