Homogenisation of free discontinuity problems: the vectorial case

Gianni Dal Maso - SISSA, Trieste
Homogenisation of free discontinuity problems: the vectorial case*

Abstract
We study deterministic and stochastic homogenisation problems for free discontinuity functionals depending on vector-valued functions under new hypotheses on the surface energies. The results are based on a compactness theorem with respect to Gamma-convergence, on the characterisation of the integrands of the Gamma-limit by means of limits of minimum values of some auxiliary minimum problems on small cubes, and on the subadditive ergodic theorem for the stochastic part.

*No previous knowledge will be assumed