Geodesic
A Probabilistic Approach to Gradient Estimates
Canadian mathematical bulletin, Tome 35 (1992) no. 1, pp. 46-55

Voir la notice de l'article provenant de la source Cambridge

DOI

Suppose u is a harmonic function on a domain D and x, x' are in D. We estimate |u(x) — u(x')| using two Brownian motions started at x and x' and killed on exiting a cube Q ⊂ D. By selecting appropriate versions of the two Brownian motions, a classical gradient estimate for u is easily derived.
DOI : 10.4153/CMB-1992-007-6
Mots-clés : 60J45. 
Cranston, M. A Probabilistic Approach to Gradient Estimates. Canadian mathematical bulletin, Tome 35 (1992) no. 1, pp. 46-55. doi: 10.4153/CMB-1992-007-6
@article{10_4153_CMB_1992_007_6,
     author = {Cranston, M.},
     title = {A {Probabilistic} {Approach} to {Gradient} {Estimates}},
     journal = {Canadian mathematical bulletin},
     pages = {46--55},
     year = {1992},
     volume = {35},
     number = {1},
     doi = {10.4153/CMB-1992-007-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-007-6/}
}
TY  - JOUR
AU  - Cranston, M.
TI  - A Probabilistic Approach to Gradient Estimates
JO  - Canadian mathematical bulletin
PY  - 1992
SP  - 46
EP  - 55
VL  - 35
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-007-6/
DO  - 10.4153/CMB-1992-007-6
ID  - 10_4153_CMB_1992_007_6
ER  - 
%0 Journal Article
%A Cranston, M.
%T A Probabilistic Approach to Gradient Estimates
%J Canadian mathematical bulletin
%D 1992
%P 46-55
%V 35
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-007-6/
%R 10.4153/CMB-1992-007-6
%F 10_4153_CMB_1992_007_6

Cité par Sources :