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. 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 ϕ.

Dalla Riva M., Molinarolo R., Musolino P. (2021). Existence results for a nonlinear nonautonomous transmission problem via domain perturbation. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS, 1-26 [10.1017/prm.2021.60].

Existence results for a nonlinear nonautonomous transmission problem via domain perturbation

Dalla Riva M.;
2021-10-01

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. 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 ϕ.
ott-2021
Settore MAT/05 - Analisi Matematica
Dalla Riva M., Molinarolo R., Musolino P. (2021). Existence results for a nonlinear nonautonomous transmission problem via domain perturbation. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS, 1-26 [10.1017/prm.2021.60].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/546030
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