Neumann problem for non-divergence elliptic and parabolic equations with BMOX coefficients in weighted sobolev spaces

Doyoon Kim, Hongjie Dong, Hong Zhang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homo-geneous Neumann boundary condition. All the leading coeffcients are assumed to be only measurable in the time variable and have small mean oscillations in the spatial variables. Our results can be applied to Neumann boundary value problems for stochastic partial differential equations with BMOx coeffcients.

Original languageEnglish
Pages (from-to)4895-4914
Number of pages20
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume36
Issue number9
DOIs
Publication statusPublished - 2016 Sep 1

Keywords

  • Lp estimates
  • Parabolic equations
  • Weighted Sobolev spaces

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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