Boundary Riesz potential estimates for elliptic equations with measurable nonlinearities. (May 2020) - Kim, Youchan; Youn, Yeonghun
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.