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Embedding operators and maximal regular differential-operator equations in Banach-valued function spaces
Journal of Inequalities and Applications volume 2005, Article number: 826085 (2005)
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.
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Shakhmurov, V.B. Embedding operators and maximal regular differential-operator equations in Banach-valued function spaces. J Inequal Appl 2005, 826085 (2005). https://doi.org/10.1155/JIA.2005.329
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