Necessary conditions for weak lower semicontinuity on domains with infinite measure
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA. firstname.lastname@example.org
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
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