Abstract
This dissertation is devoted to the study of two nonlinear nonautonomous transmission boundary value problems for the Laplace operator in perturbed domains. From a geometrical point of view, two configurations will be considered:singularly perturbed domains and regularly perturbed domains. The former are obtained by removing from a given bounded open set a portion whose size is proportional to a positive parameter close to 0, the latter are obtained by removing a portion whose form is shaped by a suitable diffeomorphism φ, which depends regularly on . Adopting a functional analytic approach, we prove real analyticity theorems for the dependence of the solutions upon the parameter that describes the singular or regular perturbation, and a local uniqueness theorem for the solutions of the singularly perturbed boundary value problem: this last, in particular, is an improvement of the uniqueness results for families of solutions typically obtained in this framework
| Date of Award | 2019 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Gennady Mishuris (Supervisor) & Adam Vellender (Supervisor) |