Necessary conditions for weak lower semicontinuity on domains with infinite measure
ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 2, pp. 457-471.

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

DOI: 10.1051/cocv/2009005
Classification: 49J45
Keywords: scalar integral functionals, weak lower semicontinuity, necessary conditions
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title = {Necessary conditions for weak lower semicontinuity on domains with infinite measure},
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Krömer, Stefan. Necessary conditions for weak lower semicontinuity on domains with infinite measure. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 2, pp. 457-471. doi : 10.1051/cocv/2009005. http://archive.numdam.org/articles/10.1051/cocv/2009005/

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