Search results for "integration by parts"
showing 2 items of 12 documents
A note on the isoperimetric inequality
2003
We show that the sharp integral form on the isoperimetric inequality holds for those orientation-preserving mappings f ∈ W l o c n 2 n + 1 ( Ω , R n ) f\in W^\frac {n^2}{n+1}_{loc}(\Omega , \mathbb {R}^n) whose Jacobians obey the rule of integration by parts.
Long-Time Behaviour for the Brownian Heat Kernel on a Compact Riemannian Manifold and Bismut’s Integration-by-Parts Formula
2007
We give a probabilistic proof of the classical long-time behaviour of the heat kernel on a compact manifold by using Bismut’s integration-by-parts formula.