Embeddings and Separable Differential Operators in Spaces of Sobolev-Lions type

Abstract

We study embedding theorems for anisotropic spaces of Bessel-Lions type H-p,gamma(l) (Omega; E-0, E), where E-0 and E are Banach spaces. We obtain the most regular spaces Ea for which mixed differentiation operators D-alpha from H-p,gamma(l)(Omega; E-0, E) to L-p,L-gamma(Omega; E-alpha) are bounded. The spaces Ea are interpolation spaces between E-0 and E, depending on alpha = (alpha(1), alpha(2), . . . , alpha n) and l = (l(1), l(2), . . . , l(n)). The results obtained are applied to prove the separability of anisotropic differential operator equations with variable coefficients.