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Existence results for a nonlinear nonautonomous transmission problem via domain perturbation
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 6 / December 2022
- Published online by Cambridge University Press:
- 11 October 2021, pp. 1451-1476
- Print publication:
- December 2022
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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 
$\phi$.
