THE FUNCTIONAL ANALYTIC APPROACH FOR QUASI-PERIODIC BOUNDARY VALUE PROBLEMS FOR THE HELMHOLTZ EQUATION

Roberto Bramati, Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino

Risultato della ricerca: Contributo su rivistaArticolo in rivistapeer review

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 originaleInglese
pagine (da-a)27-68
Numero di pagine42
RivistaAdvances in Differential Equations
Volume29
Numero di pubblicazione1-2
DOI
Stato di pubblicazionePubblicato - 2024
Pubblicato esternamente

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