PUMA
Istituto di Matematica Applicata e Tecnologie Informatiche     
Ambrosio L., Colli Franzone P., Savare' G. Gamma-convergence of a family of anisotropic functionals with lack of coercivity. Preprint ercim.cnr.ian//1998-1123, 1998.
 
 
Abstract
(English)
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 componenets of their argument. This particular feature arises from the study of the so called ``Bidomain model'' for the cardiac electric field; one of its consequence is that the $L^1$-norm of a minimizing sequence can be unbounded and therefore a lack of coercivity occours. 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.
Subject Vectorial integral functionals
Bidomain model
Cardiac electric fields



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