Laplace problem with an exponential nonlinear boundary condition

Abstract

In this paper, we establish a new result for the Laplace problem with exponential Robin boundary conditions posed on the unit disk in ${\mathbb{R}}^2$. More precisely, we prove the existence and uniqueness of a solution under suitable smallness assumptions on the boundary data. Our approach relies on an iterative method combined with periodic Sobolev embedding results.

21 pages