Embedding and maximal regular differential operators in Sobolev-Lions spaces

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Shakhmurov V. B.

ACTA MATHEMATICA SINICA-ENGLISH SERIES, vol.22, no.5, pp.1493-1508, 2006 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 22 Issue: 5
• Publication Date: 2006
• Doi Number: 10.1007/s10114-005-0764-5
• Journal Name: ACTA MATHEMATICA SINICA-ENGLISH SERIES
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.1493-1508
• Istanbul University Affiliated: No

Abstract

This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated with Banach spaces E-0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of spaces E-0 and E. In particular, the most regular class of interpolation spaces E-alpha between E-0, E depending on alpha and the order of space are found and the boundedness of differential operators D-alpha from this space to E-alpha-valued L-p,L-gamma spaces is proved. These results are applied to partial differential-operator equations with paxameters to obtain conditions that guarantee the maximal L-p,L-gamma regularity and R-positivity uniformly with respect to these parameters.