Embedding Theorems and Boundary-value Problems for cusp domains

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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 $L^{2, ξ}(\partial D)$ 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 $I_{2}:H^{1}(D)\to L^{2,ξ}(\partial D)$ i.e. on type of singularities. We obtain an exact description of the weights $ξ$ 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.
Correction of misprints: pages 5, 6, 11. We found more compact of Theorem 1, part 3, 4

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Analysis of PDEs, Functional Analysis, 35J25, 46E35

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http://salesiana.dossiersoluciones.com/handle/123456789/136194

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0706.2772
 http://arxiv.org/abs/0706.2772

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arXiv