Existence results for a nonlinear nonautonomus transmission problem via domain perturbation

Matteo Dalla Riva; Riccardo Molinarolo; Paolo Musolino

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arXiv · 2211.13105

Existence results for a nonlinear nonautonomus transmission problem via domain perturbation

Matteo Dalla Riva·Riccardo Molinarolo·Paolo Musolino

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Abstract

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 $\phi$.

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Matteo Dalla Riva, Riccardo Molinarolo, Paolo Musolino. 2022-11-23. Existence results for a nonlinear nonautonomus transmission problem via domain perturbation. https://arxiv.org/abs/2211.13105

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