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 
@article{COCV_2010__16_2_457_0,
     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},
     volume = {16},
     number = {2},
     year = {2010},
     doi = {10.1051/cocv/2009005},
     mrnumber = {2654202},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/cocv/2009005/}
}
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
PY  - 2010
SP  - 457
EP  - 471
VL  - 16
IS  - 2
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/cocv/2009005/
DO  - 10.1051/cocv/2009005
LA  - en
ID  - COCV_2010__16_2_457_0
ER  - 
%0 Journal Article
%A Krömer, Stefan
%T Necessary conditions for weak lower semicontinuity on domains with infinite measure
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2010
%P 457-471
%V 16
%N 2
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/cocv/2009005/
%R 10.1051/cocv/2009005
%G en
%F COCV_2010__16_2_457_0
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://archive.numdam.org/articles/10.1051/cocv/2009005/

[1] B. Dacorogna, Direct methods in the calculus of variations, Applied Mathematical Sciences 78. Springer, Berlin etc. (1989). | Zbl

[2] I. Fonseca and G. Leoni, Modern Methods in the Calculus of Variations: Lp Spaces, Springer Monographs in Mathematics. Springer, New York (2007). | Zbl

[3] E. Giusti, Direct methods in the calculus of variations. World Scientific, Singapore (2003). | Zbl

[4] W. Gustin, On the interior of the convex hull of an Euclidean set. Bull. Am. Math. Soc. 53 (1947) 299-301. | Zbl

[5] V.G. Maz'Ya, Sobolev spaces. Springer-Verlag, Berlin etc. (1985). | Zbl

[6] 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. Steklova 170 (1984) 233-247 (Russian). | Zbl

Cité par Sources :