Embedding operators and maximal regular differential-operator equations in Banach-valued function spaces

Abstract

This study focuses on anisotropic Sobolev type spaces associated with Banach spaces,. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of and. In particular, the most regular class of interpolation spaces between,, depending of and order of spaces are found that mixed derivatives belong with values; the boundedness and compactness of differential operators from this space to-valued spaces are proved. These results are applied to partial differential-operator equations with parameters to obtain conditions that guarantee the maximal regularity uniformly with respect to these parameters.