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Necessary conditions for weak lower semicontinuity on domains with infinite measure

Published online by Cambridge University Press:  21 April 2009

Stefan Krömer
Stefan Krömer*
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA. kroemers@andrew.cmu.edu
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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 $+\infty$.

Keywords

Scalar integral functionalsweak lower semicontinuitynecessary conditions
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 2 , April 2010 , pp. 457 - 471
Copyright
© EDP Sciences, SMAI, 2009

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References

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