On parabolic Adams's, the Chiarenza-Frasca theorems, and some other results related to parabolic Morrey spaces

We present several results of embedding type for parabolic Morrey and $ L_{p} $ spaces with or without mixed norms. Some other interpolation results for parabolic Morrey spaces are also given. The main object of investigation is the term $ b^{i}D_{i}u $ and the ways to estimate it in various Morrey...

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Bibliographic Details
Published inMathematics in engineering Vol. 5; no. 2; pp. 1 - 20
Main Author Krylov, Nicolai
Format Journal Article
LanguageEnglish
Published AIMS Press 2022
Subjects
adams theorem
chiarenza-frasca theorem
embedding theorems
parabolic morrey spaces
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ISSN2640-3501
2640-3501
DOI10.3934/mine.2023038

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Summary:We present several results of embedding type for parabolic Morrey and $ L_{p} $ spaces with or without mixed norms. Some other interpolation results for parabolic Morrey spaces are also given. The main object of investigation is the term $ b^{i}D_{i}u $ and the ways to estimate it in various Morrey and $ L_{p} $ spaces in order to be able to treat it as a perturbation term in the parabolic equations.
ISSN:2640-3501
2640-3501
DOI:10.3934/mine.2023038