Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589629 | Journal of Functional Analysis | 2016 | 45 Pages |
Abstract
Based on the idea of a recent paper by Ambrosio–Gigli–Savaré (2014) [5], we show that the L2L2-gradient flow of the q-Cheeger energy, called q-heat flow, solves a generalized gradient flow problem of the Renyi entropy functional in the p-Wasserstein. For that, a further study of the q -heat flow is presented including a condition for its mass preservation. Under a convexity assumption on the upper gradient, which holds for all q≥2q≥2, one gets uniqueness of the gradient flow and the two flows can be identified. Smooth solutions of the q-heat flow are solutions to the parabolic q -Laplace equation, i.e. ∂tft=Δqft∂tft=Δqft.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Martin Kell,