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

Nicolai Krylov; Nicolai Krylov

doi:10.3934/mine.2023038

Mathematics in Engineering

2023, Volume 5, Issue 2: 1-20. doi: 10.3934/mine.2023038

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

Nicolai Krylov ^,

School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

Received: 03 March 2022 Revised: 24 May 2022 Accepted: 24 May 2022 Published: 10 June 2022

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.
- parabolic Morrey spaces,
- embedding theorems,
- Adams theorem,
- Chiarenza-Frasca theorem
Citation: Nicolai Krylov. On parabolic Adams's, the Chiarenza-Frasca theorems, and some other results related to parabolic Morrey spaces[J]. Mathematics in Engineering, 2023, 5(2): 1-20. doi: 10.3934/mine.2023038

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Abstract

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.

References

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