Global weighted estimates for the gradient of solutions to nonlinear elliptic equations

Sun Sig Byun; Seungjin Ryu

doi:10.1016/j.anihpc.2012.08.001

Global weighted estimates for the gradient of solutions to nonlinear elliptic equations

Sun Sig Byun, Seungjin Ryu

Department of Mathematics

Seoul National University

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

68 Scopus citations

Abstract

We consider nonlinear elliptic equations of p-Laplacian type that are not necessarily of variation form when the nonlinearity is allowed to be discontinuous and the boundary of the domain can go beyond the Lipschitz category. Under smallness in the BMO nonlinearity and sufficient flatness of the Reifenberg domain, we obtain the global weighted L^q estimates with qε(p,∞) for the gradient of weak solutions.

Original language	English
Pages (from-to)	291-313
Number of pages	23
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	30
Issue number	2
DOIs	https://doi.org/10.1016/j.anihpc.2012.08.001
State	Published - 2013

Keywords

BMO space
Gradient estimate
Nonlinear elliptic equation
Reifenberg domain

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10.1016/j.anihpc.2012.08.001

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abstract = "We consider nonlinear elliptic equations of p-Laplacian type that are not necessarily of variation form when the nonlinearity is allowed to be discontinuous and the boundary of the domain can go beyond the Lipschitz category. Under smallness in the BMO nonlinearity and sufficient flatness of the Reifenberg domain, we obtain the global weighted Lq estimates with qε(p,∞) for the gradient of weak solutions.",

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AU - Ryu, Seungjin

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AB - We consider nonlinear elliptic equations of p-Laplacian type that are not necessarily of variation form when the nonlinearity is allowed to be discontinuous and the boundary of the domain can go beyond the Lipschitz category. Under smallness in the BMO nonlinearity and sufficient flatness of the Reifenberg domain, we obtain the global weighted Lq estimates with qε(p,∞) for the gradient of weak solutions.

KW - BMO space

KW - Gradient estimate

KW - Nonlinear elliptic equation

KW - Reifenberg domain

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SN - 0294-1449

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JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 2

ER -

Global weighted estimates for the gradient of solutions to nonlinear elliptic equations

Abstract

Keywords

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