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 fun-damental solution and the related layer potentials, showing how they are used to construct the solutions of quasi-periodic boundary value prob-lems, 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.
The functional analytic approach for quasi-periodic boundary value problems for the Helmholtz equation
Luzzini, Paolo;Musolino, Paolo
2024
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 fun-damental solution and the related layer potentials, showing how they are used to construct the solutions of quasi-periodic boundary value prob-lems, 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.File in questo prodotto:
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