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.

Pure mathematicsApplied MathematicsGeneral MathematicsCalculusIntegration by partsIntegral formIsoperimetric inequalityMathematicsProceedings of the American Mathematical Society
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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.

lawMathematical analysisProbabilistic proofIntegration by partsMathematics::Differential GeometryRiemannian manifoldManifold (fluid mechanics)Heat kernelBrownian motionlaw.inventionMathematics
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