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.
Citation
Roberto Bramati. Matteo Dalla Riva. Paolo Luzzini. Paolo Musolino. "The functional analytic approach for quasi-periodic boundary value problems for the Helmholtz equation." Adv. Differential Equations 29 (1/2) 27 - 68, January/Febraury 2024. https://doi.org/10.57262/ade029-0102-27
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