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arXiv · 2210.15927

The Functional Analytic Approach for quasi-periodic boundary value problems for the Helmholtz equation

Roberto Bramati·Matteo Dalla Riva·Paolo Luzzini·Paolo Musolino
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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.

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Roberto Bramati, Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino. 2022-10-28. The Functional Analytic Approach for quasi-periodic boundary value problems for the Helmholtz equation. https://arxiv.org/abs/2210.15927

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