Embedding and maximal regular differential operators in Sobolev-Lions spaces

Shakhmurov V. B.

ACTA MATHEMATICA SINICA-ENGLISH SERIES, cilt.22, sa.5, ss.1493-1508, 2006 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 5
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1007/s10114-005-0764-5
  • Dergi Adı: ACTA MATHEMATICA SINICA-ENGLISH SERIES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1493-1508
  • İstanbul Üniversitesi Adresli: Hayır

Özet

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.