Embedding and Maximal Regular Differential Operators in Sobolev-Lions Spaces

查看全文 作　　者：Veli [1]B.SHAKHMUROV

机构地区：[1]Istanbul University, Engineering Faculty, Department of Electric-Electronics Engineering,Avcilar, 34850 Istanbul, Turkey

出　　处：《Acta Mathematica Sinica,English Series》索引2006年第22卷第5期,共16页

基　　金：This work is supported by the grant of Istanbul University (Project UDP-227/18022004) 摘　　要：<正> This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated withBanach spaces E_0,E. Several conditions are found that ensure the continuity and compactness ofembedding operators that are optimal regular in these spaces in terms of interpolations of spaces E_0and E. In particular, the most regular class of interpolation spaces E_α between E_0, E depending onα and the order of space are found and the boundedness of differential operators D~α from this spaceto E_α-valued L_(ρ,γ)spaces is proved. These results are applied to partial differential-operator equationswith parameters to obtain conditions that guarantee the maximal L_(ρ,γ)regularity and R-positivityuniformly with respect to these parameters. 关键词：嵌入算子 Banach函数空间微分算子方程最大规律性算子傅立叶乘法 Banach空间插值

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Embedding and Maximal Regular Differential Operators in Sobolev-Lions Spaces

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