# 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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- I. Fonseca and G. Leoni, Modern Methods in the Calculus of Variations: Lp Spaces, Springer Monographs in Mathematics. Springer, New York (2007). Zbl1153.49001
- E. Giusti, Direct methods in the calculus of variations. World Scientific, Singapore (2003). Zbl1028.49001
- W. Gustin, On the interior of the convex hull of an Euclidean set. Bull. Am. Math. Soc.53 (1947) 299–301. Zbl0034.10502
- 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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