Work

Convergence of layer potentials and Riemann-Hilbert problem on extension domains

Year: 2024

Type: preprint

Abstract: We prove the convergence of layer potential operators for the harmonic transmission problem over a sequence of converging two-sided extension domains. Consequently, the Neumann-Poincar{é} operators, Calder{ó}n projectors, and associated Neumann series converge in this setting. As a result, we generalize the notion of Cauchy integrals and, in a sense, of Hilbert transforms for a class of extension domains. Our approach relies on dyadic approximations of arbitrary open sets, considering convergence in terms of characteristic functions, Hausdorff distance, and compact sets.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2411.03767

Authors: Claret, Gabriel, Rozanova-Pierrat, Anna, Teplyaev, Alexander

Institutions: Université Paris-Saclay, CentraleSupélec, Mathématiques et Informatique pour la Complexité et les Systèmes, University of Connecticut

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Centre National de la Recherche Scientifique, Institut national des sciences mathématiques et de leurs interactions

Award: REU Site: Fractals and Stochastics at UConn

OpenAlex ID: W4404168232

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