On the asymptotic behaviour of anisotropic energies arising in the cardiac bidomain model
Luigi Ambrosio
Scuola Normale Superiore, Pisa, ItalyGiuseppe Savaré
Università di Pavia, ItalyPiero Colli Franzone
Università di Pavia, Italy

Abstract
We study the [Gamma]-convergence of a family of vectorial integral functionals, which are the sum of a vanishing anisotropic quadratic form in the gradients and a penalizing double-well potential depending only on a linear combination of the components of their argument. This particular feature arises from the study of the so-called `bidomain model' for the cardiac electric field; one of its consequences is that the L1-norm of a minimizing sequence can be unbounded and therefore a lack of coercivity occurs. We characterize the [Gamma]-limit as a surface integral functional, whose integrand is a convex function of the normal and can be computed by solving a localized minimization problem.
Cite this article
Luigi Ambrosio, Giuseppe Savaré, Piero Colli Franzone, On the asymptotic behaviour of anisotropic energies arising in the cardiac bidomain model. Interfaces Free Bound. 2 (2000), no. 3, pp. 213–266
DOI 10.4171/IFB/19