Embedding and Maximal Regular Differential Operators in Sobolev-Lions Spaces

摘要

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.