Décomposition de l'énergie par niveau de potentiel

International audienceSeveral 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