Boundary Riesz potential estimates for elliptic equations with measurable nonlinearities

Youchan Kim; Yeonghun Youn

doi:10.1016/j.na.2019.02.001

Boundary Riesz potential estimates for elliptic equations with measurable nonlinearities

Youchan Kim, Yeonghun Youn

Department of Mathematics

Seoul National University

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

1 Scopus citations

Abstract

We consider elliptic equations with measurable nonlinearities in a half cube Q_2R∩{(x¹,x^′)∈Rⁿ:x¹>0} where the boundary data is given on Q_2R∩{(x¹,x^′)∈Rⁿ:x¹=0}. We obtain a point-wise estimate of the gradient in terms of Riesz potential of the right-hand side data and the oscillation of the gradient of the boundary data under the assumption that the nonlinearity is only allowed to be measurable in x¹-variable.

Original language	English
Article number	111445
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	194
DOIs	https://doi.org/10.1016/j.na.2019.02.001
State	Published - May 2020

Keywords

Nonlinear elliptic equations
Riesz potentials

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10.1016/j.na.2019.02.001

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title = "Boundary Riesz potential estimates for elliptic equations with measurable nonlinearities",

abstract = "We consider elliptic equations with measurable nonlinearities in a half cube Q2R∩{(x1,x′)∈Rn:x1>0} where the boundary data is given on Q2R∩{(x1,x′)∈Rn:x1=0}. We obtain a point-wise estimate of the gradient in terms of Riesz potential of the right-hand side data and the oscillation of the gradient of the boundary data under the assumption that the nonlinearity is only allowed to be measurable in x1-variable.",

keywords = "Nonlinear elliptic equations, Riesz potentials",

author = "Youchan Kim and Yeonghun Youn",

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year = "2020",

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doi = "10.1016/j.na.2019.02.001",

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AU - Youn, Yeonghun

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N2 - We consider elliptic equations with measurable nonlinearities in a half cube Q2R∩{(x1,x′)∈Rn:x1>0} where the boundary data is given on Q2R∩{(x1,x′)∈Rn:x1=0}. We obtain a point-wise estimate of the gradient in terms of Riesz potential of the right-hand side data and the oscillation of the gradient of the boundary data under the assumption that the nonlinearity is only allowed to be measurable in x1-variable.

AB - We consider elliptic equations with measurable nonlinearities in a half cube Q2R∩{(x1,x′)∈Rn:x1>0} where the boundary data is given on Q2R∩{(x1,x′)∈Rn:x1=0}. We obtain a point-wise estimate of the gradient in terms of Riesz potential of the right-hand side data and the oscillation of the gradient of the boundary data under the assumption that the nonlinearity is only allowed to be measurable in x1-variable.

KW - Nonlinear elliptic equations

KW - Riesz potentials

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U2 - 10.1016/j.na.2019.02.001

DO - 10.1016/j.na.2019.02.001

M3 - Article

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VL - 194

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

M1 - 111445

ER -

Boundary Riesz potential estimates for elliptic equations with measurable nonlinearities

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