On the Existence of Smooth Solutions for Fully Nonlinear Parabolic Equations with Measurable "Coefficients" without Convexity Assumptions

Hongjie Dong, N. V. Krylov

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in any cylindrical smooth domain with smooth boundary data one can find an approximating equation which has a unique continuous solution with the first derivatives bounded and the second spacial derivatives locally bounded. The approximating equation is constructed in such a way that it modifies the original one only for large values of the unknown function and its spacial derivatives.

Original languageEnglish (US)
Pages (from-to)1038-1068
Number of pages31
JournalCommunications in Partial Differential Equations
Volume38
Issue number6
DOIs
StatePublished - Jun 2013

Bibliographical note

Funding Information:
The authors are sincerely grateful to the referee for his very quick report and helpful comments on an earlier version of the manuscript. H. Dong was partially supported by NSF Grant DMS-1056737. N. V. Krylov was partially supported by NSF Grant DMS-1160569

Keywords

  • Bellman's equations
  • Finite differences
  • Fully nonlinear parabolic equations

Fingerprint

Dive into the research topics of 'On the Existence of Smooth Solutions for Fully Nonlinear Parabolic Equations with Measurable "Coefficients" without Convexity Assumptions'. Together they form a unique fingerprint.

Cite this