Boundary Riesz potential estimates for elliptic equations with measurable nonlinearities. (May 2020)

• Record Type: Journal Article
• Authors: Kim, Youchan; Youn, Yeonghun
• Is Part Of: Nonlinear analysis. Volume 194(2020)
• Publication Date: 2020-05
• Subjects: primary 35J60 -- secondary 35B65 35R05; Nonlinear elliptic equations -- Riesz potentials; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.02.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider elliptic equations with measurable nonlinearities in a half cube Q 2 R ∩ { ( x 1, x ′ ) ∈ R n : x 1 > 0 } where the boundary data is given on Q 2 R ∩ { ( x 1, x ′ ) ∈ R n : x 1 = 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 x 1 -variable.