The marriage of analytic power to geometric intuition drives many of today's mathematical
advances, yet books that build the connection from an elementary level remain scarce. This …

This book deals with a class of mathematical problems which involve the minimization of the
sum of a volume and a surface energy and have lately been refered to as' free discontinuity …

Imaging is an interdisciplinary research area with profound applications in many areas of
science, engineering, technology, and medicine. The most primitive form of imaging is visual …

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 notion of \calA-quasiconvexity is introduced as a necessary and sufficient condition for
(sequential) lower semicontinuity of (u, v) ↦ Ω f (x, u (x), v (x))\, dx whenever …

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 …

The paper is concerned with the fine properties of functions in, the space of functions with
bounded deformation. We analyse the set of Lebesgue points and the set where these …

arXiv:1007.3770v1 [math.FA] 21 Jul 2010 Page 1 arXiv:1007.3770v1 [math.FA] 21 Jul 2010
Gamma-convergence of nonlocal perimeter functionals Luigi Ambrosio∗ Scuola Normale …

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 …

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 …