no. 2
Necessary conditions for weak lower semicontinuity on domains with infinite measure
ESAIM: Control, Optimisation and Calculus of Variations, Tome 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 +∞.

DOI : 10.1051/cocv/2009005
Classification : 49J45
Mots clés : scalar integral functionals, weak lower semicontinuity, necessary conditions 
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     author = {Kr\"omer, Stefan},
     title = {Necessary conditions for weak lower semicontinuity on domains with infinite measure},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {457--471},
     publisher = {EDP-Sciences},
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     year = {2010},
     doi = {10.1051/cocv/2009005},
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     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv/2009005/}
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Krömer, Stefan. Necessary conditions for weak lower semicontinuity on domains with infinite measure. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 2, pp. 457-471. doi : 10.1051/cocv/2009005. http://www.numdam.org/articles/10.1051/cocv/2009005/

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