# An entropy generation formula on $$\varvec{RCD(K,\infty )}$$ R C D ( K , ∞ ) spaces

An entropy generation formula on $$\varvec{RCD(K,\infty )}$$ R C D ( K , ∞ ) spaces J. Feng and T. Nguyen have shown that the solutions of the Fokker–Planck equation in $$\mathbf{R}^d$$ R d satisfy an entropy generation formula. We prove that, in compact metric measure spaces with the $$RCD(K,\infty )$$ R C D ( K , ∞ ) property, a similar result holds for curves of measures whose density is bounded away from zero and infinity. We use this fact to show the existence of minimal characteristics for the stochastic value function. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Differential Equations and Applications NoDEA Springer Journals

# An entropy generation formula on $$\varvec{RCD(K,\infty )}$$ R C D ( K , ∞ ) spaces

, Volume 25 (4) – Jun 5, 2018
33 pages

/lp/springer_journal/an-entropy-generation-formula-on-varvec-rcd-k-infty-r-c-d-k-spaces-RnbK3m5IgQ
Publisher
Springer Journals
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis
ISSN
1021-9722
eISSN
1420-9004
D.O.I.
10.1007/s00030-018-0518-6
Publisher site
See Article on Publisher Site

### Abstract

J. Feng and T. Nguyen have shown that the solutions of the Fokker–Planck equation in $$\mathbf{R}^d$$ R d satisfy an entropy generation formula. We prove that, in compact metric measure spaces with the $$RCD(K,\infty )$$ R C D ( K , ∞ ) property, a similar result holds for curves of measures whose density is bounded away from zero and infinity. We use this fact to show the existence of minimal characteristics for the stochastic value function.

### Journal

Nonlinear Differential Equations and Applications NoDEASpringer Journals

Published: Jun 5, 2018

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations