Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others

Doyoon Kim, N. V. Krylov

Research output: Contribution to journalArticle

65 Citations (Scopus)

Abstract

We prove the unique solvability of second order elliptic equations in nondivergence form in Sobolev spaces. The coefficients of the second order terms are measurable in one variable and VMO in other variables. From this result, we obtain the weak uniqueness of the Martingale problem associated with the elliptic equations.

Original languageEnglish
Pages (from-to)489-506
Number of pages18
JournalSIAM Journal on Mathematical Analysis
Volume39
Issue number2
DOIs
Publication statusPublished - 2007 Dec 1
Externally publishedYes

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Keywords

  • Martingale problem
  • Second order equations
  • Vanishing mean oscillation

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics
  • Numerical Analysis

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