For the purpose of these lectures, a microstructure is any structure on a scale between the
macroscopic scale (on which we usually make observations) and the atomic scale. Such …

Publisher Summary This chapter discusses the main properties of Γ-convergence, in
particular those that are useful in the actual computation of Γ-limits. For some classes of …

In this paper we consider a non-local anisotropic model for phase separation in two-phase
fluids at equilibrium, and show that when the thickness of the interface tends to zero in a …

Surface measures in Carnot-Carathéodory spaces Page 1 Digital Object Identifier (DOI)
10.1007/s005260000076 Calc. Var. 13, 339–376 (2001) Surface measures in Carnot-Carathéodory …

Viscosity methods for minimization problems are revisited from some modern perspectives
in variational analysis. Variational convergences for sequences of functions (epi …

This paper is an extended version of the lecture delivered at the Summer School on
Differential Equations and Calculus of Variations (Pisa, September 16–28, 1996). That …

The parametrized indicator measures and the Brunn-Minkowski inequality are used to prove
that the Wulff set W‪‪‪‪‪ г‪ is a minimizer for the surface energy where the density is the support …

Given a function u: Ω⊆ _ ℝ n→ ℝ, we introduce a notion of total variation of u depending on
a possibly discontinuous Finsler metric. We prove some integral representation results for …

∫ϵ^-1(1-|∇u|^2)^2+ϵ|∇∇u|^2 in two space dimensions. We introduce a new scheme for
proving lower bounds and show the bounds are asymptotically sharp for certain domains …

We provide the general outline of an analysis of the motion of diffuse interfaces in the order-
parameter (phase field) formulation which includes nondifferentiable and nonconvex …