On the Robin problem for the Laplace equation in multiply connected domains
Analysis of PDEs
2026-02-18 v1
Abstract
This paper complements the existing theory developed in [5] for the Dirichlet and Neumann problems for the Laplace equation, in multiply connected domains. Within the framework of layer potential methods, we study the Laplace equation under Robin boundary conditions, representing the solutions by means of a double layer potential. We observe that the classical approach searches the solutions in terms of a single layer potential.
Keywords
Cite
@article{arxiv.2602.15647,
title = {On the Robin problem for the Laplace equation in multiply connected domains},
author = {Alberto Cialdea and Vita Leonessa},
journal= {arXiv preprint arXiv:2602.15647},
year = {2026}
}
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12 pages