Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth

Hongjie Dong, Doyoon Kim

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

We establish global regularity for weak solutions to quasilinear divergence form elliptic and parabolic equations over Lipschitz domains with controlled growth conditions on low order terms. The leading coefficients belong to the class of BMO functions with small mean oscillations with respect to x.

Original languageEnglish
Pages (from-to)1750-1777
Number of pages28
JournalCommunications in Partial Differential Equations
Volume36
Issue number10
DOIs
Publication statusPublished - 2011 Oct 1
Externally publishedYes

Fingerprint

Global Regularity
Quasilinear Parabolic Equations
Lipschitz Domains
Quasilinear Elliptic Equation
Growth Conditions
Elliptic Equations
Parabolic Equation
Weak Solution
Divergence
Oscillation
Coefficient
Term
Class
Form

Keywords

  • BMO coefficients
  • Boundary value problems
  • Quasilinear elliptic and parabolic equations
  • Sobolev spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth. / Dong, Hongjie; Kim, Doyoon.

In: Communications in Partial Differential Equations, Vol. 36, No. 10, 01.10.2011, p. 1750-1777.

Research output: Contribution to journalArticle

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