Singular limit phenomenon in a nonlinear elliptic problem arising in electrochemistry

Fernández Martínez D (2026)

Publication Language: English

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2026

URI: https://arxiv.org/abs/2606.20619

DOI: 10.48550/arXiv.2606.20619

Open Access Link: https://arxiv.org/abs/2606.20619

Abstract

We study a singularly perturbed harmonic problem, with nonlinear Neumann boundary conditions of signed exponential type, arising in galvanic corrosion applications. We focus on the low-conductivity regime, which leads to a singular limit in which the solution presents a jump in the boundary. We prove convergence of the solution traces in the corresponding fractional Sobolev spaces, identify the interior limit solution, and obtain a sharp logarithmic energy expansion for smooth boundary junctions. The proofs rely mostly on trace Moser-Trudinger estimates for showing well-posedness and regularity, and on mollifier approximation techniques for the singular limit analysis. Numerical experiments test the predicted convergence rate.

Authors with CRIS profile

Daniel Fernández Martínez Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

How to cite

APA:

Fernández Martínez, D. (2026). Singular limit phenomenon in a nonlinear elliptic problem arising in electrochemistry. (Unpublished, Submitted).

MLA:

Fernández Martínez, Daniel. Singular limit phenomenon in a nonlinear elliptic problem arising in electrochemistry. Unpublished, Submitted. 2026.

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