Weak lower semicontinuity by means of anisotropic parametrized measures

2017/04/02 by Kałamajska, Agnieszka, Krömer, Stefan, Kružík, Martin · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.00368

Abstract

It is well known that besides oscillations, sequences bounded only in L¹ can also develop concentrations, and if the latter occurs, we can at most hope for weak^* convergence in the sense of measures. Here we derive a new tool to handle mutual interferences of an oscillating and concentrating sequence with another weakly converging sequence. We introduce a couple of explicit examples showing a variety of possible kinds of behavior and outline some applications in Sobolev spaces.

Cited by

• Relaxation of variational problems in the space of functions with bounded B-variation: interaction with measures and lack of concentration phenomena

Related

• Liftings, Young measures, and lower semicontinuity
• Oscillations and concentrations up to the boundary
• Strengthening of weak convergence for Radon measures in separable Banach spaces
• Strong approximation of partial sums under dependence conditions with application to dynamical systems
• Lower semicontinuity via W^1,q-quasiconvexity