Shakhmurov, Veli B.2024-05-252024-05-25201510133-38521588-273X10.1007/s10476-015-0303-22-s2.0-84949798352https://doi.org/10.1007/s10476-015-0303-2https://hdl.handle.net/20.500.14517/310We introduce the vector-valued Sobolev spaces W-m,W-p(x) (Omega; E-0, E) with variable exponent associated with two Banach spaces E-0 and E. The most regular space E-alpha is found such that the differential operator D-alpha is bounded and compact from W-m,W-p(x)(Omega; E-0, E) to L-q(x)(Omega; E-alpha ), where E-alpha are interpolation spaces between E-0 and E is depending on alpha = (alpha(1), alpha(2),..., alpha(n)) and the positive integer m, where Omega subset of R-n is a region such that there exists a bounded linear extension operator from W-m,W-p(x) (Omega; E-0, E) to W-m,W-p(x) (R-n; E(A), E). The function p(x) is Lipschitz continuous on Omega and q(x) is a measurable function such that 1 < p(x) <= q(x) <= np(x)/n-mp(x) for a.e. x is an element of(Omega) over bar. Ehrling-Nirenberg-Gagilardo type sharp estimates for mixed derivatives are obtained. Then, by using this embedding result, the separability properties of abstract differential equations are established.eninfo:eu-repo/semantics/closedAccess[No Keyword Available]ArticleQ3Q3414273297WOS:000366630800003