Calculus of Variations and Geometric Measure Theory
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A. Baldi - B. Franchi

Maxwell's equations in anisotropic media and Maxwell's equations in Carnot groups as variational limits

created by franchib on 29 Nov 2011

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Inserted: 29 nov 2011
Last Updated: 29 nov 2011

Year: 2011

Abstract:

Let $\mathbb G$ be a free Carnot group (i.e. a connected simply connected nilpotent stratified free Lie group) of step 2. In this paper, we prove that the variational functional generated by ``intrinsic'' Maxwell's equations in $\mathbb G$ is the $\Gamma$-limit of a sequence of classical (i.e. Euclidean) variational functionals associated with strongly anisotropic dielectric permittivity and magnetic permeability in the Euclidean space.


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