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 …

We present, analyze, and implement a new method for the design of the stiffest structure
subject to a pressure load or a given field of internal forces. Our structure is represented as a …

For a general class of diffuse anisotropic multi-phase order parameter (or phase-field)
models we use formally matched asymptotic expansions to determine the asymptotic limit …

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 …

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 …

A notion of total variation depending on a metric with discontinuous coefficients -
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∫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 …

We study Γ-convergence of graph-based Ginzburg–Landau functionals, both the limit for
zero diffusive interface parameter ε→ 0 and the limit for infinite nodes in the graph m→∞ …

We introduce a new concept, the Young measure on micropatterns, to study singularly
perturbed variational problems that lead to multiple small scales depending on a small …