Geodesic
On the asymptotic behaviour of anisotropic energies arising in the cardiac bidomain model
Luigi Ambrosio1 ; Piero Colli Franzone2 ; Giuseppe Savaré2
1Scuola Normale Superiore, Pisa, Italy
2Università di Pavia, Italy
Interfaces and free boundaries, Tome 2 (2000) no. 3, pp. 213-266

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DOI

We study the Γ-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 Γ-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.
DOI : 10.4171/ifb/19
Classification : 46-XX, 60-XX
Mots-clés : localized minimization problems; anisotropic energies; cardiac bidomain model

Luigi Ambrosio  1   ; Piero Colli Franzone  2   ; Giuseppe Savaré  2

1 Scuola Normale Superiore, Pisa, Italy
2 Università di Pavia, Italy 
Luigi Ambrosio; Piero Colli Franzone; Giuseppe Savaré. On the asymptotic behaviour of anisotropic energies arising in the cardiac bidomain model. Interfaces and free boundaries, Tome 2 (2000) no. 3, pp. 213-266. doi: 10.4171/ifb/19
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