English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The aim of this paper is twofold. In the setting of $RCD(K,\infty)$ metricmeasure spaces, we derive uniform gradient and Laplacian contraction estimatesalong solutions of the viscous approximation of the Hamilton-Jacobi equation.We use these estimates to prove that, as the viscosity tends to zero, solutionsof this equation converge to the evolution driven by the Hopf-Lax formula, inaccordance with the smooth case. We then use such convergence to study thesmall-time Large Deviation Principle for both the heat kernel and the Brownianmotion: we obtain the expected behaviour under the additional assumption thatthe space is proper.

Viscosity solutions of Hamilton-Jacobi equation in $RCD(K,\infty)$ spaces and applications to large deviations