Calculus of Variations and Geometric Measure Theory

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

Existence results for a nonlinear nonautonomus transmission problem via domain perturbation

created by molinarolo on 24 Nov 2022


Published Paper

Inserted: 24 nov 2022
Last Updated: 24 nov 2022

Journal: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Pages: 1-26
Year: 2021
Doi: 10.1017/prm.2021.60

ArXiv: 2211.13105 PDF


In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$. First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$.