Embedding Theorems and Boundary-value Problems for cusp domains

Details Embedding Theorems and Boundary-value Problems for cusp domains Embedding Theorems and Boundary-value Problems for cusp domains

2007-06-19

arxiv.org/abs/0706.2772v2

Mathematics

Analysis of PDEs

Correction of misprints: pages 5, 6, 11. We found more compact of Theorem 1, part 3, 4

Scientific paper

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 bounded domains with 'outside peaks' on its boundaries. This result allows us to formulate correctly the corresponding Robin boundary-value problems for elliptic operators.

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