Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms

N. V. Krylov

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66 Scopus citations

Abstract

An Lq (Lp)-theory of divergence and non-divergence form parabolic equations is presented. The main coefficients are supposed to belong to the class VMOx, which, in particular, contains all measurable functions depending only on t. The method of proving simplifies the methods previously used in the case p = q.

Original languageEnglish (US)
Pages (from-to)521-558
Number of pages38
JournalJournal of Functional Analysis
Volume250
Issue number2
DOIs
StatePublished - Sep 15 2007

Bibliographical note

Funding Information:
✩ The work was partially supported by NSF Grants DMS-0140405 and DMS-0653121. E-mail address: krylov@math.umn.edu.

Keywords

  • Mixed norms
  • Second-order equations
  • Vanishing mean oscillation

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