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

Hongjie Dong; Doyoon Kim

doi:10.1080/03605302.2011.571746

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

Hongjie Dong, Doyoon Kim

Research output: Contribution to journal › Article › peer-review

28 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 language	English
Pages (from-to)	1750-1777
Number of pages	28
Journal	Communications in Partial Differential Equations
Volume	36
Issue number	10
DOIs	https://doi.org/10.1080/03605302.2011.571746
Publication status	Published - 2011 Oct
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/03605302.2011.571746

Cite this

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title = "Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth",

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.",

keywords = "BMO coefficients, Boundary value problems, Quasilinear elliptic and parabolic equations, Sobolev spaces",

author = "Hongjie Dong and Doyoon Kim",

note = "Funding Information: We would like to thank Dian K. Palagachev for informing us his recent papers [32, 33], and the anonymous referees for their helpful comments. H. Dong was partially supported by NSF grant number DMS-0800129.",

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AU - Dong, Hongjie

AU - Kim, Doyoon

N1 - Funding Information: We would like to thank Dian K. Palagachev for informing us his recent papers [32, 33], and the anonymous referees for their helpful comments. H. Dong was partially supported by NSF grant number DMS-0800129.

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AB - 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.

KW - BMO coefficients

KW - Boundary value problems

KW - Quasilinear elliptic and parabolic equations

KW - Sobolev spaces

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JO - Communications in Partial Differential Equations

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

Abstract

Keywords

ASJC Scopus subject areas

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