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Necessary conditions for weak lower semicontinuityon domains with infinite measure

Published online by Cambridge University Press:  21 April 2009

Stefan Krömer*
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA. [email protected]
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Abstract

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 ${\mathbb R}^N$ . An emphasis is put on domains with infinite measure, and the integrand is allowed to assume the value $+\infty$ .

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2009

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