Open Access
2024 Improved regularity for the stochastic fast diffusion equation
Ioana Ciotir, Dan Goreac, Jonas M. Tölle
Author Affiliations +
Electron. Commun. Probab. 29: 1-7 (2024). DOI: 10.1214/24-ECP575


We prove that the solution to the singular-degenerate stochastic fast-diffusion equation with parameter m(0,1), with zero Dirichlet boundary conditions on a bounded domain in any spatial dimension, and driven by linear multiplicative Wiener noise, exhibits improved regularity in the Sobolev space W01,m+1 for initial data in L2.

Funding Statement

IC was partially supported by l’Agence Nationale de la Recherche (ANR), project ANR COSS number ANR-22-CE40-0010. DG has been partially supported by the NSF of Shandong Province (NO. ZR202306020015), National Key R and D Program of China (NO. 2018YFA0703900), and the NSF of P.R. China (NO. 12031009). The research of JMT was partially supported by the seed funding grant UNA Random of the Una Europa alliance.


Download Citation

Ioana Ciotir. Dan Goreac. Jonas M. Tölle. "Improved regularity for the stochastic fast diffusion equation." Electron. Commun. Probab. 29 1 - 7, 2024.


Received: 3 October 2023; Accepted: 4 February 2024; Published: 2024
First available in Project Euclid: 22 February 2024

arXiv: 2310.01328
Digital Object Identifier: 10.1214/24-ECP575

Primary: 35B65 , 35K67 , 60H15 , 76S05

Keywords: improved Sobolev regularity , linear multiplicative Wiener noise , stochastic fast diffusion equation , Stochastic partial differential equation , stochastic singular-degenerate diffusion equation

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