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

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.

arXiv commentTo appear in Inverse Problems

References in corpus (4)

• The stability for the Cauchy problem for elliptic equations
• An inverse boundary value problem for certain anisotropic quasilinear elliptic equations
• A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem
• A phase-field approach for the interface reconstruction in a nonlinear elliptic problem arising from cardiac electrophysiology