Necessary conditions for weak lower semicontinuity on domains with infinite measure
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 16, Issue: 2, page 457-471
- ISSN: 1292-8119
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topKrömer, Stefan. "Necessary conditions for weak lower semicontinuity on domains with infinite measure." ESAIM: Control, Optimisation and Calculus of Variations 16.2 (2010): 457-471. <http://eudml.org/doc/250704>.
@article{Krömer2010,
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 $+\infty$.
},
author = {Krömer, Stefan},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Scalar integral functionals; weak lower semicontinuity; necessary conditions; scalar integral functionals; domains with infinite measure},
language = {eng},
month = {4},
number = {2},
pages = {457-471},
publisher = {EDP Sciences},
title = {Necessary conditions for weak lower semicontinuity on domains with infinite measure},
url = {http://eudml.org/doc/250704},
volume = {16},
year = {2010},
}
TY - JOUR
AU - Krömer, Stefan
TI - Necessary conditions for weak lower semicontinuity on domains with infinite measure
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/4//
PB - EDP Sciences
VL - 16
IS - 2
SP - 457
EP - 471
AB -
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 $+\infty$.
LA - eng
KW - Scalar integral functionals; weak lower semicontinuity; necessary conditions; scalar integral functionals; domains with infinite measure
UR - http://eudml.org/doc/250704
ER -
References
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- V.G. Maz'ya, Sobolev spaces. Springer-Verlag, Berlin etc. (1985).
- Yu.S. Nikol'skij, Integral estimates for differentiable functions on unbounded domains. Proc. Steklov Inst. Math.170 (1987) 267–283. Translation from Tr. Mat. Inst. Steklova170 (1984) 233–247 (Russian).
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