On divergence form second-order pdes with growing coefficients in W 1 p spaces without weights

N. V. Krylov

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Abstract

We consider second-order divergence form uniformly parabolic and elliptic PDEs with bounded and VMOx leading coefficients and possibly linearly growing lower-order coefficients. We look for solutions which are summable to the pth power with respect to the usual Lebesgue measure along with their first derivatives with respect to the spatial variables.

Original languageEnglish (US)
Title of host publicationProgress in Nonlinear Differential Equations and Their Application
PublisherSpringer US
Pages389-414
Number of pages26
DOIs
StatePublished - 2011

Publication series

NameProgress in Nonlinear Differential Equations and Their Application
Volume80
ISSN (Print)1421-1750
ISSN (Electronic)2374-0280

Bibliographical note

Funding Information:
The work was partially supported by NSF grant DMS-0653121.

Keywords

  • Divergence type equations
  • Growing coefficients
  • Sobolev spaces without weights
  • Stochastic partial differential equations

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