Compact embedding in Besov spaces and B-separable elleptic operators
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Date
2010
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Publisher
Science Press
Abstract
Necessary and sufficient conditions for compactness of sets in Banach space valued Besov class B (p,q) (s) (Omega;E) is derived. The embedding theorems in Besov-Lions type spaces B (p,q) (l,s) (Omega;E (0), E) are studied, where E (0), E are two Banach spaces and E (0) aS, E. The most regular class of interpolation space E (alpha) , between E (0) and E are found such that the mixed differential operator D (alpha) is bounded and compact from B (p,q) (l,s) (Omega;E (0),E) to B (p,q) (s) (Omega;E (alpha) ) and Ehrling-Nirenberg-Gagliardo type sharp estimates established. By using these results the separability of differential operators with variable coefficients and the maximal B-regularity of parabolic Cauchy problem are obtained. In applications, the infinite systems of the elliptic partial differential equations and parabolic Cauchy problems are studied.
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Keywords
embedding theorems, Banach-valued function spaces, differential-operator equations, maximal B-regularity, operator-valued Fourier multipliers, interpolation of Banach spaces, abstract parabolic Cauchy problem
Turkish CoHE Thesis Center URL
WoS Q
Q1
Scopus Q
Q1
Source
Volume
53
Issue
4
Start Page
1067
End Page
1084