Calculus of Variations and Geometric Measure Theory

A. Garroni - V. Nesi - M. Ponsiglione

Dielectric breakdown: optimal bounds

created on 04 Jan 2002


Published Paper

Inserted: 4 jan 2002

Journal: Proc. R. Soc. Lond. A
Volume: 457
Pages: 2317-2335
Year: 2001


We study dielectric breakdown for composites made of two isotropic phases. We show that Sachs' bound is optimal. This simple example is used to illustrate a variational principle which departs from the traditional one. We also derive the usual variational principle by elementary means without appealing to the technology of convex duality.

Keywords: $\Gamma$-convergence, composites, bounds, Dielectric breakdown, variational principle in $L^\infty$