ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS

doi:10.1016/S0252-9602(11)60207-5

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 49-67.doi: 10.1016/S0252-9602(11)60207-5

ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS

Veli Shakhmurov

Department of Electronics Engineering and Communication, Okan University, Akfirat Beldesi, Tuzla, 34959, Istanbul, Turkey

收稿日期:2007-06-19 修回日期:2009-09-27 出版日期:2011-01-20 发布日期:2011-01-20

ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS

Veli Shakhmurov

Department of Electronics Engineering and Communication, Okan University, Akfirat Beldesi, Tuzla, 34959, Istanbul, Turkey

Received:2007-06-19 Revised:2009-09-27 Online:2011-01-20 Published:2011-01-20

摘要/Abstract

摘要：

The weighted Sobolev-Lions type spaces W ^l_p, _γ(Ω; E₀, E) = W ^l_p, _γ (Ω; E) \ L_p_, _γ(Ω; E₀) are two Banach spaces and E₀ is continuously and densely embedded on E. A new concept of capacity of region Ω∈Rⁿ in W ^l_p, _γ (Ω; 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 E_α between E₀ and E, depending of α and l, are found such that mixed differential operators D^α are bounded and compact from W ^l_p, γ(Ω; E₀, E) to E_α-valued L_p, γ spaces. In applications, the maximal regularity for differential-operator equations with parameters are studied.

关键词: Capacity of regions, embedding theorems, Banach-valued function spaces, differential-operator equations, Semigroups of operators, operator-valued Fourier multipliers, interpolation of Banach spaces

Abstract:

Key words: Capacity of regions, embedding theorems, Banach-valued function spaces, differential-operator equations, Semigroups of operators, operator-valued Fourier multipliers, interpolation of Banach spaces

中图分类号:

34G10

Veli Shakhmurov. ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS[J]. 数学物理学报(英文版), 2011, 31(1): 49-67.

Veli Shakhmurov. ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS[J]. Acta mathematica scientia,Series B, 2011, 31(1): 49-67.

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ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS

ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS

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