Embedding operators and boundary-value problems for rough domains

Details Embedding operators and boundary-value problems for rough domains Embedding operators and boundary-value problems for rough domains

2004-11-08

arxiv.org/abs/math/0411176v1

Mathematics

Analysis of PDEs

Scientific paper

In 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.

Affiliated with

Also associated with

No associations

Rating

Embedding operators and boundary-value problems for rough domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Embedding operators and boundary-value problems for rough domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Embedding operators and boundary-value problems for rough domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-367508