Probabilités/Théorie du potentiel
Marches aléatoires et théorie du potentiel dans les domaines lipschitziens
[Random walks and potential theory in Lipschitz domains]
Comptes Rendus. Mathématique, Volume 337 (2003) no. 9, pp. 615-618.

We give a technical estimate on the gradients of the Green's functions in Lipschitz domains. The main application is a sharp Central Limit Theorem for random walks in these domains.

On donne des estimations techniques sur les gradients de fonctions de Green dans des domaines lipschitziens. L'application principale de ces estimations est un théorème central limite optimal de marches aléatoires dans ces domaines.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2003.08.008
Varopoulos, Nicholas Th. 1

1 Université Pierre et Marie Curie (Paris 6) et I.U.F., département de mathématiques (UFR 920), boı̂te courrier 172, 4, place Jussieu, 75252 Paris cedex 05, France
@article{CRMATH_2003__337_9_615_0,
     author = {Varopoulos, Nicholas Th.},
     title = {Marches al\'eatoires et th\'eorie du potentiel dans les domaines lipschitziens},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {615--618},
     publisher = {Elsevier},
     volume = {337},
     number = {9},
     year = {2003},
     doi = {10.1016/j.crma.2003.08.008},
     language = {fr},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2003.08.008/}
}
TY  - JOUR
AU  - Varopoulos, Nicholas Th.
TI  - Marches aléatoires et théorie du potentiel dans les domaines lipschitziens
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 615
EP  - 618
VL  - 337
IS  - 9
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2003.08.008/
DO  - 10.1016/j.crma.2003.08.008
LA  - fr
ID  - CRMATH_2003__337_9_615_0
ER  - 
%0 Journal Article
%A Varopoulos, Nicholas Th.
%T Marches aléatoires et théorie du potentiel dans les domaines lipschitziens
%J Comptes Rendus. Mathématique
%D 2003
%P 615-618
%V 337
%N 9
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2003.08.008/
%R 10.1016/j.crma.2003.08.008
%G fr
%F CRMATH_2003__337_9_615_0
Varopoulos, Nicholas Th. Marches aléatoires et théorie du potentiel dans les domaines lipschitziens. Comptes Rendus. Mathématique, Volume 337 (2003) no. 9, pp. 615-618. doi : 10.1016/j.crma.2003.08.008. http://www.numdam.org/articles/10.1016/j.crma.2003.08.008/

[1] Bensoussan, A.; Lions, J.-L.; Papanicolaou, G. Asymptotic Analysis for Periodic Structures, North-Holland, 1978

[2] Bers, L.; John, F.; Schechter, M. Partial Differential Equations, Wiley, 1964

[3] Dahlberg, B.E.J.; Kenig, C.E.; Verchota, A.C. The Dirichlet problem for the biharmonic equation in a Lipschitz domain, Ann. Inst. Fourier (Grenoble), Volume 36 (1986) no. 3, pp. 109-135

[4] W. Feller, An Introduction to Probability Theory, Vol. 2, Wiley

[5] Kadlec, J. The regularity of the solution of the Poisson problem in a domain whose boundary is similar to a convex domain, Czechoslovak Math. J., Volume 14 (1964), pp. 386-393

[6] Varopoulos, N.Th. Potential theory in Lipschitz domains, Canad. J. Math., Volume 53 (2001) no. 5, pp. 1057-1120

[7] Zhikov, V.V. A spectral approach to the asymptotic problem of diffusion, Differentsial'nye Uravneniya, Volume 25 (1985) no. 1, pp. 44-55

Cited by Sources: