Abstract
The embedding theorems in anisotropic Besov-Lions type spaces are studied; here and are two Banach spaces. The most regular spaces are found such that the mixed differential operators are bounded from to , where are interpolation spaces between and depending on and . By using these results the separability of anisotropic differential-operator equations with dependent coefficients in principal part and the maximal -regularity of parabolic Cauchy problem are obtained. In applications, the infinite systems of the quasielliptic partial differential equations and the parabolic Cauchy problems are studied.
Highlights
Embedding theorems in function spaces have been studied in [8, 35, 37, 38]
In the second step we prove that the embedding Blp+,θs (Rn; E) ⊂ WlBsp,θ(Rn; E) is continuous
By virtue of Definition 2.1 it is clear that the inequality (3.23) will follow immediately from (3.31) if we can prove that the operator-function Ψ =αA1−κ−μ[hμ(A + η)]−1 is a multiplier in
Summary
Embedding theorems in function spaces have been studied in [8, 35, 37, 38]. A comprehensive introduction to the theory of embedding of function spaces and historical references may be found in [37]. The most regular interpolation class Eα between E0 and E is found such that the appropriate mixed differential operators Dα are bounded from Blp+,qs(Rn; E0, E) to Bsp,q(Rn; Eα) By applying these results the maximal regularity of certain class of anisotropic partial DOE with varying coefficients in Banachvalued Besov spaces is derived. By using these results the maximal B-regularity of the parabolic Cauchy problem is shown.
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