Integral Varadhan formula for non-linear heat flow

Ohta, Shin-ichi; Suzuki, Kohei

Abstract

We prove the integral Varadhan short-time formula for non-linear heat flow on measured Finsler manifolds. To the best of the authors' knowledge, this is the first result establishing a Varadhan-type formula for non-linear semigroups. We do not assume the reversibility of the metric, thus the distance function can be asymmetric. Within this generality, we reveal that the probabilistic interpretation is well-suited for our formula; the probability that a particle starting from a set A can be found in another set B describes the distance from A to B. One side of the estimates (the upper bound of the probability) is also established in the nonsmooth setting of infinitesimally strictly convex metric measure spaces.

Citation

Ohta, S.-I., & Suzuki, K. (2025). Integral Varadhan formula for non-linear heat flow. Journal of Functional Analysis, 289(8), Article 110983. https://doi.org/10.1016/j.jfa.2025.110983

• Journal Article Type: Article
• Acceptance Date: Mar 28, 2025
• Online Publication Date: Apr 3, 2025
• Publication Date: Oct 15, 2025
• Deposit Date: May 12, 2025
• Publicly Available Date: May 12, 2025
• Journal: Journal of Functional Analysis
• Print ISSN: 0022-1236
• Electronic ISSN: 1096-0783
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 289
• Issue: 8
• Article Number: 110983
• DOI: https://doi.org/10.1016/j.jfa.2025.110983
• Public URL: https://durham-repository.worktribe.com/output/3789887