Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces

Hongjie Dong, Doyoon Kim

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We consider both divergence and non-divergence parabolic equations on a half space in weighted Sobolev spaces. All the leading coefficients are assumed to be only measurable in the time and one spatial variable except one coefficient, which is assumed to be only measurable either in the time or the spatial variable. As functions of the other variables the coefficients have small bounded mean oscillation (BMO) semi-norms. The lower-order coefficients are allowed to blow up near the boundary with a certain optimal growth condition. As a corollary, we also obtain the corresponding results for elliptic equations.

Original languageEnglish
Pages (from-to)681-735
Number of pages55
JournalAdvances in Mathematics
Volume274
DOIs
Publication statusPublished - 2015 Apr 9
Externally publishedYes

Fingerprint

Weighted Sobolev Spaces
Elliptic Equations
Parabolic Equation
Coefficient
Bounded Mean Oscillation
Optimal Growth
Seminorm
Growth Conditions
Half-space
Blow-up
Divergence
Corollary

Keywords

  • Elliptic and parabolic equations
  • Measurable coefficients
  • Weighted Sobolev spaces

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces. / Dong, Hongjie; Kim, Doyoon.

In: Advances in Mathematics, Vol. 274, 09.04.2015, p. 681-735.

Research output: Contribution to journalArticle

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