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Embedding and Maximal Regular Differential Operators in Sobolev–Lions Spaces

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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 α between E 0, E depending on α and the order of space are found and the boundedness of differential operators D α from this space to Eα–valued L p,γ spaces is proved. These results are applied to partial differential–operator equations with parameters to obtain conditions that guarantee the maximal L p,γ regularity and R–positivity uniformly with respect to these parameters.

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Authors and Affiliations

  1. Istanbul University, Engineering Faculty, Department of Electric–Electronics Engineering, Avcilar, 34850, Istanbul, Turkey

    Veli B. Shakhmurov

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  1. Veli B. Shakhmurov
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Correspondence to Veli B. Shakhmurov.

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This work is supported by the grant of Istanbul University (Project UDP-227/18022004)

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Shakhmurov, V.B. Embedding and Maximal Regular Differential Operators in Sobolev–Lions Spaces. Acta Math Sinica 22, 1493–1508 (2006). https://doi.org/10.1007/s10114-005-0764-5

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