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- Title
Existence results for a nonlinear nonautonomous transmission problem via domain perturbation.
- Authors
Dalla Riva, Matteo; Molinarolo, Riccardo; Musolino, Paolo
- 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 $\phi$.
- Subjects
BOUNDARY value problems; DIFFERENTIAL inclusions; NONLINEAR operators
- Publication
Proceedings of the Royal Society of Edinburgh: Section A: Mathematics, 2022, Vol 152, Issue 6, p1451
- ISSN
0308-2105
- Publication type
Article
- DOI
10.1017/prm.2021.60