5 papers · 1 filter
On an inverse problem with applications in cardiac electrophysiology
Andrea Aspri, Elena Beretta, Elisa Francini +2
In this paper, we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the forward problem, we show that perfectly insulating regi…
Normalized solutions for Sobolev critical Schrödinger equations on bounded domains
Dario Pierotti, Gianmaria Verzini, Junwei Yu
We study the existence and multiplicity of positive solutions with prescribed -norm for the Sobolev critical Schrödinger equation on a bounded domain , $…
On the reconstruction of cavities in a nonlinear model arising from cardiac electrophysiology
Elena Beretta, M. Cristina Cerutti, Dario Pierotti +1
In this paper, we deal with the problem of determining perfectly insulating regions (cavities) from one boundary measurement in a nonlinear elliptic equation arising from cardiac e…
Normalized bound states for the nonlinear Schrodinger equation in bounded domains
Dario Pierotti, Gianmaria Verzini
Given , we study the elliptic problem \[ \text{find } (U,λ)\in H^1_0(Ω)\times \mathbb{R} \text{ such that } \begin{cases} -ΔU+λU=|U|^{p-1}U \int_Ω U^2\, dx=ρ, \end{cases} \] w…
On a semilinear elliptic boundary value problem arising in cardiac electrophysiology
Elena Beretta, M. Cristina Cerutti, Andrea Manzoni +1
In this paper we provide a representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction in a simplified {\em mon…