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 …

This book is developed for the study of vectorial problems in the calculus of variations. The
subject is a very active one and almost half of the book consists of new material. This is a …

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 calculus of variations is one of the oldest subjects in mathematics, and it is very much
alive and still evolving. Besides its mathematical importance and its links to other branches …

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 …

We study semicontinuity of multiple integrals∫ Ω f (x, u, Du) dx, where the vector-valued
function u is defined for x ε Ω ⊂ R^ n with values in ℝ N. The function f (x, s, ξ) is assumed to …

In a first period the Young measures were developed to get a correct notion of generalized
solutions. Now they give new methods to handle uniformly integrable or bounded …

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 …

Integral representation of relaxed energies and of Γ-limits of functionals (u,
v)\mapsto\int_\Omega f (x, u (x), v (x))\, dx are obtained when sequences of fields v may …

The study of fuzzy variational problems has received significant attention over the past
decade due to its successful applications in numerous fields, such as image segmentation …