Boundary Riesz potential estimates for elliptic equations with measurable nonlinearities

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...

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Bibliographic Details
Published in:Nonlinear analysis 2020-05, Vol.194, p.111445, Article 111445
Main Authors: Kim, Youchan, Youn, Yeonghun
Format: Article
Language:English
Subjects:
Elliptic functions
Mathematical analysis
Nonlinear elliptic equations
Riesz potentials
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Summary: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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2019.02.001