The calculus of variations has its roots in the first problems of optimality studied in classical
antiquity by Archimedes (ca. 287–212 BC in Syracuse, Magna Graecia) and Zenodorus (ca …

We show that positively 1-homogeneous rank one convex functions are convex at 0 and at
matrices of rank one. The result is a special case of an abstract convexity result that we …

In this article we derive an (almost) optimal scaling law for a singular perturbation problem
associated with the Tartar square. As in Winter (Eur J Appl Math 8 (2): 185–207, 1997) …

We present a systematic treatment of the theory of Compensated Compactness under
Murat's constant rank assumption. We give a short proof of a sharp weak lower …

Deciding whether a given function is quasiconvex is generally a difficult task. Here, we
discuss a number of numerical approaches that can be used in the search for a …

We consider the following question arising in the theory of differential inclusions: Given an
elliptic set and a Sobolev map u whose gradient lies in the quasiconformal envelope of and …

Inspired by Morrey's Problem (on rank-one convex functionals) and the Burkholder integrals
(of his martingale theory) we find that the Burkholder functionals $\text {B} _p $, $ p\geqslant …

In this article we study quantitative rigidity properties for the compatible and incompatible
two-state problems for suitable classes of A-free differential inclusions and for a singularly …

We consider Morrey's open question whether rank-one convexity already implies
quasiconvexity in the planar case. For some specific families of energies, there are precise …

Shape-memory alloys are materials undergoing a first-order, diffusionless, solid–solid phase
transformation that is accompanied by a reduction of symmetry, giving rise to rich …