Riesz potential type estimates for nonlinear elliptic equations

Youchan Kim

doi:10.1016/j.jde.2017.07.031

Riesz potential type estimates for nonlinear elliptic equations

Youchan Kim

Department of Mathematics

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

4 Scopus citations

Abstract

For p≥2, we study nonlinear elliptic equations of p-Laplacian type with measure data div a(Du,u,x)=μ in Ω when the nonlinearity depends on the variable of the possibly unbounded solution itself. We obtain the point-wise gradient bound and the gradient continuity in terms of a certain Riesz potential of the right-hand side measure.

Original language	English
Pages (from-to)	6844-6884
Number of pages	41
Journal	Journal of Differential Equations
Volume	263
Issue number	10
DOIs	https://doi.org/10.1016/j.jde.2017.07.031
State	Published - 15 Nov 2017

Keywords

Nonlinear elliptic equations
Riesz potential type estimates

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10.1016/j.jde.2017.07.031

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title = "Riesz potential type estimates for nonlinear elliptic equations",

abstract = "For p≥2, we study nonlinear elliptic equations of p-Laplacian type with measure data div a(Du,u,x)=μ in Ω when the nonlinearity depends on the variable of the possibly unbounded solution itself. We obtain the point-wise gradient bound and the gradient continuity in terms of a certain Riesz potential of the right-hand side measure.",

keywords = "Nonlinear elliptic equations, Riesz potential type estimates",

author = "Youchan Kim",

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year = "2017",

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AU - Kim, Youchan

PY - 2017/11/15

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N2 - For p≥2, we study nonlinear elliptic equations of p-Laplacian type with measure data div a(Du,u,x)=μ in Ω when the nonlinearity depends on the variable of the possibly unbounded solution itself. We obtain the point-wise gradient bound and the gradient continuity in terms of a certain Riesz potential of the right-hand side measure.

AB - For p≥2, we study nonlinear elliptic equations of p-Laplacian type with measure data div a(Du,u,x)=μ in Ω when the nonlinearity depends on the variable of the possibly unbounded solution itself. We obtain the point-wise gradient bound and the gradient continuity in terms of a certain Riesz potential of the right-hand side measure.

KW - Nonlinear elliptic equations

KW - Riesz potential type estimates

UR - http://www.scopus.com/inward/record.url?scp=85028296921&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2017.07.031

DO - 10.1016/j.jde.2017.07.031

M3 - Article

AN - SCOPUS:85028296921

SN - 0022-0396

VL - 263

SP - 6844

EP - 6884

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 10

ER -

Riesz potential type estimates for nonlinear elliptic equations

Abstract

Keywords

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