Nonlinear transmission problems for the Laplace operator
: a functional analytic approach

  • Riccardo Molinarolo

Student thesis: Doctoral ThesisDoctor of Philosophy


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 Award2019
Original languageEnglish
Awarding Institution
  • Aberystwyth University
SupervisorGennady Mishuris (Supervisor) & Adam Vellender (Supervisor)

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