| Issue |
ESAIM: COCV
Volume 16, Number 2, April-June 2010
|
|
|---|---|---|
| Page(s) | 457 - 471 | |
| DOI | https://doi.org/10.1051/cocv/2009005 | |
| Published online | 21 April 2009 | |
Necessary conditions for weak lower semicontinuity on domains with infinite measure
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA. kroemers@andrew.cmu.edu
Received:
8
August
2008
Revised:
23
December
2008
We derive sharp necessary conditions for weak sequential lower semicontinuity of integral functionals on Sobolev spaces, with an integrand which only depends on the gradient of a scalar field over a domain in 
. An emphasis is put on domains with infinite measure, and the integrand is allowed to assume the value 
.
Mathematics Subject Classification: 49J45
Key words: Scalar integral functionals / weak lower semicontinuity / necessary conditions
© EDP Sciences, SMAI, 2009
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