Microstructure is a feature of crystals with multiple symmetry-related energy-minimizing
states. Continuum models have been developed explaining microstructure as the mixture of …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same
compactness properties that finite dimensional spaces do: basically, bounded sequences …

The relaxation method has enjoyed an intensive development during many decades and
this new edition of this comprehensive text reflects in particular the main achievements in the …

Oscillatory properties of a weak convergent sequence of functions bounded in L p, 1≤
p≤∞, may be summarized by the parametrized measure it generates. When such a …

Nonlinear partial differential equations has become one of the main tools of mod ern
mathematical analysis; in spite of seemingly contradictory terminology, the subject of …

The underlying mathematical problems in nonlinear elasticity are fascinating. The variational
methods developed to tackle them are even more so. The graduate student and the …

We prove that the quasiconvex envelope of a differentiable function which satisfies natural
growth conditions at infinity is a C^1 function. Without the growth conditions the result fails in …

The first objective of this work is to present, to some extent, a deep introduction to the basic
concepts on real and functional analysis. In principle, the text is written for applied …

We consider the following question: given a set of matrices with no rank-one connections,
does it support a nontrivial Young measure limit of gradients? Our main results are these:(a) …