RUBIO DE FRANCIA EXTRAPOLATION THEOREM AND RELATED TOPICS IN THE THEORY OF ELLIPTIC AND PARABOLIC EQUATIONS. A SURVEY

N. V. Krylov

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2 Scopus citations

Abstract

This is a brief historical overview of the Sobolev mixed norm theory of linear elliptic and parabolic equations and the recent development in this theory based on the Rubio de Francia extrapolation theorem. A self-contained proof of this theorem along with other relevant tools of Real Analysis are also presented as well as an application to mixed norm estimates for fully nonlinear equations.

Original languageEnglish (US)
Pages (from-to)389-413
Number of pages25
JournalSt. Petersburg Mathematical Journal
Volume32
Issue number3
DOIs
StatePublished - 2021

Bibliographical note

Funding Information:
The author is sincerely grateful to Hongjie Dong who read the first draft of the paper and whose comments allowed the author to avoid several errors and misrepresentations. The author also wishes to thank P. Stinga and J. Sauer for a fruitful discussion and for providing additional relevant references.

Publisher Copyright:
© 2021 American Mathematical Society. All Rights Reserved.

Keywords

  • Rubio de Francia extrapolation theorem
  • mixed norm estimates

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