Embedding Theorems and Boundary-value Problems for cusp domains

@article{Goldshtein2007EmbeddingTA,
  title={Embedding Theorems and Boundary-value Problems for cusp domains},
  author={V. Gol'dshtein and Michail Vasiltchik},
  journal={arXiv: Analysis of PDEs},
  year={2007}
}
We study the Robin boundary-value problem for bounded domains with isolated singularities. Because for such domains trace spaces of space $H^1(D)$ on its boundaries are weighted Sobolev spaces $L^{2, \xi}(\partial D)$ existence and uniqueness of corresponding Robin boundary-value problems depends on properties of embedding operators $I_1: H^{1}(D)\to L^{2}(D)$ and $I_{2}:H^{1}(D)\to L^{2,\xi}(\partial D)$ i.e. on type of singularities. We obtain an exact description of the weights $\xi$ for… Expand
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