The weighted Sobolev-Lions type spaces W pl,γ（Ω; E0, E） = W pl,γ（Ω; E） ∩ Lp,γ （Ω; E0） are studied, where E0, E are two Banach spaces and E0 is continuously and densely embedded on E. A new concept of capa...The weighted Sobolev-Lions type spaces W pl,γ（Ω; E0, E） = W pl,γ（Ω; E） ∩ Lp,γ （Ω; E0） are studied, where E0, E are two Banach spaces and E0 is continuously and densely embedded on E. A new concept of capacity of region Ω ∈ Rn in W pl,γ（; E0, E） is introduced. Several conditions in terms of capacity of region Ω and interpolations of E0 and E are found such that ensure the continuity and compactness of embedding operators. In particular, the most regular class of interpolation spaces Eα between E0 and E, depending of α and l, are found such that mixed differential operators Dα are bounded and compact from W pl,γ（Ω; E0, E） to Eα-valued Lp,γ spaces. In applications, the maximal regularity for differential-operator equations with parameters are studied.展开更多
Necessary and sufficient conditions for compactness of sets in Banach space valued Besov class Bp,q s(Ω;E) is derived.The embedding theorems in Besov-Lions type spaces B l,s p,q(Ω;E0,E) are studied,where E0,E are tw...Necessary and sufficient conditions for compactness of sets in Banach space valued Besov class Bp,q s(Ω;E) is derived.The embedding theorems in Besov-Lions type spaces B l,s p,q(Ω;E0,E) are studied,where E0,E are two Banach spaces and E 0 E.The most regular class of interpolation space E α,between E 0 and E are found such that the mixed differential operator D α is bounded and compact from B p,q l,s (Ω;E 0,E) to B p,q s (Ω;E α) 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.展开更多
The free boundary value problems for elliptic differential-operator equations are studied.Several conditions for the uniform maximal regularity with respect to boundary parameters and the Fredholmness in abstract L p-...The free boundary value problems for elliptic differential-operator equations are studied.Several conditions for the uniform maximal regularity with respect to boundary parameters and the Fredholmness in abstract L p-spaces are given.In application,the nonlocal free boundary problems for finite or infinite systems of elliptic and anisotropic type equations are studied.展开更多
In this study, the estimates of approximation numbers of embedding operators in weighted spaces have been analyzed. These estimates depend on orders of differential operators, dimensions of function spaces and weighte...In this study, the estimates of approximation numbers of embedding operators in weighted spaces have been analyzed. These estimates depend on orders of differential operators, dimensions of function spaces and weighted functions. This fact implies that the associated embedding operators belong to Schatten class of compact operators. By using these estimates, the discreetness of spectrum and completion of root elements relating to principal nonselfedjoint degenerate differential operators is obtained.展开更多
This paper focuses on nonlocal integral boundary value problems for elliptic differential-operator equations. Here given conditions guarantee that maximal regularity and Fredholmness in L_p spaces. These results are a...This paper focuses on nonlocal integral boundary value problems for elliptic differential-operator equations. Here given conditions guarantee that maximal regularity and Fredholmness in L_p spaces. These results are applied to the Cauchy problem for abstract parabolic equations, its infinite systems and boundary value problems for anisotropic partial differential equations in mixed L_p norm.展开更多
文摘The weighted Sobolev-Lions type spaces W pl,γ（Ω; E0, E） = W pl,γ（Ω; E） ∩ Lp,γ （Ω; E0） are studied, where E0, E are two Banach spaces and E0 is continuously and densely embedded on E. A new concept of capacity of region Ω ∈ Rn in W pl,γ（; E0, E） is introduced. Several conditions in terms of capacity of region Ω and interpolations of E0 and E are found such that ensure the continuity and compactness of embedding operators. In particular, the most regular class of interpolation spaces Eα between E0 and E, depending of α and l, are found such that mixed differential operators Dα are bounded and compact from W pl,γ（Ω; E0, E） to Eα-valued Lp,γ spaces. In applications, the maximal regularity for differential-operator equations with parameters are studied.
文摘Necessary and sufficient conditions for compactness of sets in Banach space valued Besov class Bp,q s(Ω;E) is derived.The embedding theorems in Besov-Lions type spaces B l,s p,q(Ω;E0,E) are studied,where E0,E are two Banach spaces and E 0 E.The most regular class of interpolation space E α,between E 0 and E are found such that the mixed differential operator D α is bounded and compact from B p,q l,s (Ω;E 0,E) to B p,q s (Ω;E α) 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.
文摘The free boundary value problems for elliptic differential-operator equations are studied.Several conditions for the uniform maximal regularity with respect to boundary parameters and the Fredholmness in abstract L p-spaces are given.In application,the nonlocal free boundary problems for finite or infinite systems of elliptic and anisotropic type equations are studied.
文摘In this study, the estimates of approximation numbers of embedding operators in weighted spaces have been analyzed. These estimates depend on orders of differential operators, dimensions of function spaces and weighted functions. This fact implies that the associated embedding operators belong to Schatten class of compact operators. By using these estimates, the discreetness of spectrum and completion of root elements relating to principal nonselfedjoint degenerate differential operators is obtained.
文摘This paper focuses on nonlocal integral boundary value problems for elliptic differential-operator equations. Here given conditions guarantee that maximal regularity and Fredholmness in L_p spaces. These results are applied to the Cauchy problem for abstract parabolic equations, its infinite systems and boundary value problems for anisotropic partial differential equations in mixed L_p norm.
