Calculus of Variations and Geometric Measure Theory

R. Molinarolo

Existence of solutions for a singularly perturbed nonlinear non-autonomous transmission problem

created by molinarolo on 24 Nov 2022


Published Paper

Inserted: 24 nov 2022
Last Updated: 24 nov 2022

Journal: Electronic Journal of Differential Equations
Volume: 2019
Number: 53
Pages: 1-29
Year: 2019

ArXiv: 2211.12533 PDF


In this paper we analyse a boundary value problem for the Laplace equation with a nonlinear non-autonomous transmission conditions on the boundary of a small inclusion of size $\epsilon$. We show that the problem has solutions for $\epsilon$ small enough and we investigate the dependence of a specific family of solutions upon $\epsilon$. By adopting a functional analytic approach we prove that the map which takes $\epsilon$ to (suitable restrictions of) the corresponding solution can be represented in terms of real analytic functions.