Geodesic
A Haar-Rado type theorem for minimizers in Sobolev spaces
ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 1133-1143 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

Let u∈ϕ+W 0 1,1 (Ω) be a minimum for

I(v)=∫ Ω g(x,v(x))+f(∇v(x))dx
where f is convex, v↦g(x,v) is convex for a.e. x. We prove that u shares the same modulus of continuity of ϕ whenever Ω is sufficiently regular, the right derivative of g satisfies a suitable monotonicity assumption and the following inequality holds
∀γ∈∂Ω|u(x)-ϕ(γ)|≤ω(|x-γ|)a.e.x∈Ω.
This result generalizes the classical Haar-Rado theorem for Lipschitz functions.

DOI : 10.1051/cocv/2010038
Classification : 49K20
Keywords: Hölder, regularity, Lipschitz 
@article{COCV_2011__17_4_1133_0,
     author = {Mariconda, Carlo and Treu, Giulia},
     title = {A {Haar-Rado} type theorem for minimizers in {Sobolev} spaces},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1133--1143},
     year = {2011},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {4},
     doi = {10.1051/cocv/2010038},
     mrnumber = {2859868},
     zbl = {1239.49031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010038/}
}
TY  - JOUR
AU  - Mariconda, Carlo
AU  - Treu, Giulia
TI  - A Haar-Rado type theorem for minimizers in Sobolev spaces
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2011
SP  - 1133
EP  - 1143
VL  - 17
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010038/
DO  - 10.1051/cocv/2010038
LA  - en
ID  - COCV_2011__17_4_1133_0
ER  - 
%0 Journal Article
%A Mariconda, Carlo
%A Treu, Giulia
%T A Haar-Rado type theorem for minimizers in Sobolev spaces
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2011
%P 1133-1143
%V 17
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010038/
%R 10.1051/cocv/2010038
%G en
%F COCV_2011__17_4_1133_0
Mariconda, Carlo; Treu, Giulia. A Haar-Rado type theorem for minimizers in Sobolev spaces. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 1133-1143. doi: 10.1051/cocv/2010038

Cité par Sources :