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 …

Generalized Young measures as introduced by DiPerna and Majda (Commun Math Phys
108: 667–689, 1987) provide a quantitative tool for studying the one-point statistics of …

Minimization is a recurring theme in many mathematical disciplines ranging from pure to
applied. Of particular importance is the minimization of integral functionals, which is studied …

DiPerna's and Majda's generalization of Young measures is used to describe oscillations
and concentrations in sequences of maps. This convergence holds, for example, under …

This work establishes a characterization theorem for (generalized) Young measures
generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of …

Let Q be a Lipschitz domain in R n and let f∈ L∞(Q). We investigate conditions under which
the functional I n (φ)=∫ Q|∇ φ| n+ f (x) det∇ φ dx obeys I n≥ 0 for all φ∈ W 0 1, n (Q, R n) …

We state necessary and sufficient conditions for weak lower semicontinuity of integral
functionals of the form u↦∫ Ω h⁢(x, u⁢(x))⁢ dx, where h is continuous and possesses a …

arxiv:1712.08897v1 [math.AP] 24 Dec 2017 Page 1 arxiv:1712.08897v1 [math.AP] 24 Dec
2017 ON THE STRUCTURE OF MEASURES CONSTRAINED BY LINEAR PDES GUIDO DE …

We characterize generalized Young measures, the so-called DiPerna–Majda measures
which are generated by sequences of gradients. In particular, we precisely describe these …

For an integral functional defined on functions (u, v)∈ W 1, 1× L 1 featuring a prototypical
strong interaction term between u and v, we calculate its relaxation in the space of functions …