On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains

Hongjie Dong, N. V. Krylov, Xu Li

Research output: Contribution to journalArticlepeer-review

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Abstract

The solvability in the Sobolev spaces W1,2p, p > d +1, of the terminalboundary value problem is proved for a class of fully nonlinear parabolic equations, including parabolic Bellman's equations, in bounded cylindrical domains, in the case of VMO " coefficients" . The solvability in W2p, p > d, of the corresponding elliptic boundary-value problem is also obtained.

Original languageEnglish (US)
Pages (from-to)39-69
Number of pages31
JournalSt. Petersburg Mathematical Journal
Volume24
Issue number1
DOIs
StatePublished - Jan 1 2013

Keywords

  • Bellman's equations
  • Fully nonlinear elliptic and parabolic equations
  • Vanishing mean oscillation

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