The functional analytic approach for quasi-periodic boundary value problems for the Helmholtz equation

DOI10.57262/ade029-0102-27arXiv2210.15927OpenAlexW4386880543MaRDI QIDQ6187490

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

Publication date: 15 January 2024

Published in: Advances in Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.15927

zbMATH Keywords

Helmholtz equationquasi-periodic boundary value problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Cites Work

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• A real analyticity result for a nonlinear integral operator
• Weakly singular and microscopically hypersingular load perturbation for a nonlinear traction boundary value problem: a functional analytic approach
• On the evaluation of quasi-periodic Green functions and wave-scattering at and around Rayleigh-Wood anomalies
• Perturbation analysis of the effective conductivity of a periodic composite
• Polarization and moment tensors. With applications to inverse problems and effective medium theory
• Singular perturbation Dirichlet problem in a double-periodic perforated plane
• Potential and scattering theory on wildly perturbed domains
• The Green's function for the two-dimensional Helmholtz equation in periodic domains
• Asymptotic behaviour of the conformal representation of a Jordan domain with a small hole in Schauder spaces
• Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Vol. II. Transl. from the German by Boris Plamenevskii
• A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary
• Analytic dependence of a periodic analog of a fundamental solution upon the periodicity parameters
• Converging expansions for Lipschitz self-similar perforations of a plane sector
• Spectral gaps in the Dirichlet and Neumann problems on the plane perforated by a doubleperiodic family of circular holes
• Subwavelength phononic bandgap opening in bubbly media
• Topological derivatives in shape optimization
• Green's kernels and meso-scale approximations in perforated domains
• Subwavelength guided modes for acoustic waves in bubbly crystals with a line defect
• Local uniqueness of the solutions for a singularly perturbed nonlinear nonautonomous transmission problem
• On the properties of quasi-periodic boundary integral operators for the Helmholtz equation
• The Dirichlet problem in a planar domain with two moderately close holes
• Lattice sums and the two-dimensional, periodic Green's function for the Helmholtz equation
• Interactions Between Moderately Close Inclusions for the Two-Dimensional Dirichlet–Laplacian
• A singularly perturbed Dirichlet problem for the Laplace operator in a periodically perforated domain. A functional analytic approach
• A mixed problem for the Laplace operator in a domain with moderately close holes
• Asymptotic behaviour of the solutions of a non-linear transmission problem for the Laplace operator in a domain with a small hole. A functional analytic approach
• Layer Potential Techniques in Spectral Analysis. Part II: Sensitivity Analysis of Spectral Properties of High Contrast Band‐Gap Materials
• INTERACTIONS BETWEEN MODERATELY CLOSE INCLUSIONS FOR THE LAPLACE EQUATION
• Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain
• Source-neutral Green'functions for periodic problems in electrostatics, and their equivalents in electromagnetism
• A Mathematical and Numerical Framework for Bubble Meta-Screens
• Three-dimensional quasi-periodic shifted Green function throughout the spectrum, including Wood anomalies
• Stokes flow in a singularly perturbed exterior domain
• A singularly perturbed nonlinear Robin problem in a periodically perforated domain: a functional analytic approach†
• Global representation and multiscale expansion for the Dirichlet problem in a domain with a small hole close to the boundary
• Singularly Perturbed Boundary Value Problems
• Shape analyticity and singular perturbations for layer potential operators
• High Order Topological Asymptotics: Reconciling Layer Potentials and Compound Asymptotic Expansions
• Regularizing properties of space‐periodic layer heat potentials and applications to boundary value problems in periodic domains
• Domain Decomposition for Quasi-Periodic Scattering by Layered Media via Robust Boundary-Integral Equations at All Frequencies
• Selfsimilar Perturbation near a Corner: Matching Versus Multiscale Expansions for a Model Problem
• Series expansion for the effective conductivity of a periodic dilute composite with thermal resistance at the two-phase interface
• Integral Equation Methods in Scattering Theory
• Asymptotic behavior of the solutions of a nonlinear Robin problem for the Laplace operator in a domain with a small hole: a functional analytic approach
• Asymptotic behavior of the solutions of the Dirichlet problem for the Laplace operator in a domain with a small hole. A functional analytic approach

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