Abstract
We lay down the preliminary work to apply the Functional Analytic Approach to quasi-periodic boundary value problems for the Helmholtz equation. This consists in introducing a quasi-periodic fundamental solution and the related layer potentials, showing how they are used to construct the solutions of quasi-periodic boundary value problems, and how they behave when we perform a singular perturbation of the domain. To show an application, we study a nonlinear quasi-periodic Robin problem in a domain with a set of holes that shrink to points.
Lingua originale | Inglese |
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pagine (da-a) | 27-68 |
Numero di pagine | 42 |
Rivista | Advances in Differential Equations |
Volume | 29 |
Numero di pubblicazione | 1-2 |
DOI | |
Stato di pubblicazione | Pubblicato - 2024 |
Pubblicato esternamente | Sì |