Nonlinear transmission problems for the Laplace operator

: a functional analytic approach

Crynodeb

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

Dyddiad Dyfarnu	2019
Iaith wreiddiol	Saesneg
Sefydliad Dyfarnu	Prifysgol Aberystwyth
Goruchwyliwr	Gennady Mishuris (Goruchwylydd) & Adam Vellender (Goruchwylydd)