Oscillations and concentrations in sequences of gradients
Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland; Agnieszka.Kalamajska@mimuw.edu.pl
2 Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic. Corresponding address Pod vodárenskou věží 4, 182 08 Praha 8, Czech Republic.
3 Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 166 29 Praha 6, Czech Republic; email@example.com (corresponding author).
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.
Mathematics Subject Classification: 49J45 / 35B05
Key words: Sequences of gradients / concentrations / oscillations / quasiconvexity
© EDP Sciences, SMAI, 2007