Several extensions of the following classical property are studied : Let m be the Lebesgue measure on $R^d$, and let u be in $L^2_{loc}(R^d)$ such that its partial derivatives in the sense of distributions be in $L^2(R^d)$. Then the image of the measure $grad^2 u.m$ is absolutely continuous with respect to Lebesgue measure on R.
Publié le : 1983-06-20
Classification:
energy image density property,
occupation density,
local time,
Dirichlet form,
MSC 60Hxx 46Fxx 31-XX,
[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA],
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00448731,
author = {Bouleau, Nicolas},
title = {D\'ecomposition de l'\'energie par niveau de potentiel},
journal = {HAL},
volume = {1983},
number = {0},
year = {1983},
language = {fr},
url = {http://dml.mathdoc.fr/item/hal-00448731}
}
Bouleau, Nicolas. Décomposition de l'énergie par niveau de potentiel. HAL, Tome 1983 (1983) no. 0, . http://gdmltest.u-ga.fr/item/hal-00448731/