Parabolic and elliptic equations with VMO coefficients

N. V. Krylov

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181 Scopus citations

Abstract

An Lp-theory of divergence and non-divergence form elliptic and parabolic equations is presented. The main coefficients are supposed to belong to the class VMOx, which, in particular, contains all functions independent of x. Weak uniqueness of the martingale problem associated with such equations is obtained.

Original languageEnglish (US)
Pages (from-to)453-475
Number of pages23
JournalCommunications in Partial Differential Equations
Volume32
Issue number3
DOIs
StatePublished - Mar 2007

Bibliographical note

Funding Information:
The work was partially supported by NSF Grant DMS-0140405.

Keywords

  • Martingale problem
  • Second-order equations
  • Vanishing mean oscillation

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