EMBEDDING THEOREMS AND BOUNDARY-VALUE PROBLEMS FOR CUSP DOMAINS

We study the Robin boundary-value problem for bounded domains with isolated singularities. Because trace spaces of space W-2(1)(D) on boundaries of such domains are weighted Sobolev spaces L-2,L-xi(partial derivative D), existence and uniqueness of corresponding Robin boundary-value problems depends on properties of embedding operators I-perpendicular to : W-2(1)(D) -> L-2 (D) and I-2 : W-2(1)(D) -> L-2,L-xi (partial derivative D) i.e. oil types of singularities. We obtain an exact description of weights for bounded domains with 'outside peaks' oil its boundaries. This result, allows us to formulate correctly the corresponding Robin boundary-value problems for elliptic operators. Using compactness of embedding operators I-1, I-2, we prove also that these Robin boundary-value problems with the spectral parameter are of Fredholm type.