Calculus of Variations and Geometric Measure Theory

M. Dalla Riva - R. Molinarolo - P. Musolino

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

created by molinarolo on 24 Nov 2022


Published Paper

Inserted: 24 nov 2022
Last Updated: 24 nov 2022

Journal: Nonlinear Analysis
Volume: 191
Number: 111645
Year: 2020
Doi: 10.1016/

ArXiv: 2211.12818 PDF


We consider the Laplace equation in a domain of $\mathbb{R}^n$, $n\ge 3$, with a small inclusion of size $\epsilon$. On the boundary of the inclusion we define a nonlinear nonautonomous transmission condition. For $\epsilon$ small enough one can prove that the problem has solutions. In this paper, we study the local uniqueness of such solutions.