Embedding operators and maximal regular differential-operator equations in Banach-valued function spaces
By Veli B. Shakhmurov. 2005
51 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a4b994f070eab5afa4ae778d1c10529592b7bad8
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- A note on the anisotropic generalizations of the Sobolev and Morrey embedding theorems (2009, background): “It is worth pointing out that our notion of ’anisotropy’ differs from the usual concept of anisotropic spaces, as presented for instance in [7] or [12], where (nonmixed) partial derivatives of different orders in different directions are considered.”