Acta mathematica scientia, Series B >
ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS
Received date: 2007-06-19
Revised date: 2009-09-27
Online published: 2011-01-20
The weighted Sobolev-Lions type spaces W lp, γ(Ω; E0, E) = W lp, γ (Ω; E) \ Lp, 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 lp, 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 Eα between E0 and E, depending of α and l, are found such that mixed differential operators Dα are bounded and compact from W lp, γ(Ω; E0, E) to Eα-valued Lp, γ spaces. In applications, the maximal regularity for differential-operator equations with parameters are studied.
Veli Shakhmurov . ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS[J]. Acta mathematica scientia, Series B, 2011 , 31(1) : 49 -67 . DOI: 10.1016/S0252-9602(11)60207-5
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