Issue |
ESAIM: COCV
Volume 14, Number 1, January-March 2008
|
|
---|---|---|
Page(s) | 71 - 104 | |
DOI | https://doi.org/10.1051/cocv:2007051 | |
Published online | 21 September 2007 |
Oscillations and concentrations in sequences of gradients
1
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; kruzik@utia.cas.cz (corresponding author).
Received:
18
July
2006
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
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