Oscillations and concentrations in sequences of gradients
Agnieszka Kałamajska, Martin Kružík · ESAIM Control Optimisation and Calculus of Variations · 2007
We use DiPerna's and Majda's generalization of Young measures to describe oscillations and concentrations in sequences of gradients, , bounded in if p > 1 and is a bounded domain with the extension property in . Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of Ω are required and links with lower semicontinuity results by Meyers and by Acerbi and Fusco are also discussed.