On a nonlinear model in domains with cavities arising from cardiac electrophysiology

TL;DR

This paper addresses the challenge of identifying insulating cavities within cardiac tissue using boundary data, establishing well-posedness and uniqueness in a nonlinear elliptic model relevant to cardiac electrophysiology.

Contribution

It introduces a novel analysis of the inverse problem for nonlinear elliptic equations with minimal cavity regularity assumptions, proving both well-posedness and uniqueness.

Findings

Proved well-posedness of the direct problem.

Established uniqueness for the inverse problem.

Applicable to cavities with minimal regularity.

Abstract

In this paper we deal with the problem of determining perfectly insulating regions (cavities) from boundary measurements in a nonlinear elliptic equation arising from cardiac electrophysiology. With minimal regularity assumptions on the cavities, we first show well-posedness of the direct problem and then prove uniqueness for the inverse problem.