Local uniqueness of the solutions for a singularly perturbed nonlinear nonautonomous transmission problem

Abstract

We consider the Laplace equation in a domain of Rn, n≥3, with a small inclusion of size ϵ. On the boundary of the inclusion we define a nonlinear nonautonomous transmission condition. For ϵ small enough one can prove that the problem has solutions. In this paper, we study the local uniqueness of such solutions.