Existence and Smoothness of the Density for the Stochastic Continuity Equation

Author(s)

Mollinedo, David A. C. ^[1] ; Olivera, Christian ^[2] ; Tudor, Ciprian A. ^{[3, 4]}

Affiliation

^[1] Univ Tecnol Fed Parana, Curitiba, Parana - Brazil

^[2] Univ Estadual Campinas, Dept Matemat, Campinas, SP - Brazil

^[3] Univ Lille 1, UFR Math, Lille - France

^[4] Romanian Acad, ISMMA, Bucharest - Romania

• Document type: Journal article
• Source: Results in Mathematics; v. 74, n. 1 MAR 2019.
• Web of Science Citations: 0

Abstract

We consider the stochastic continuity equation driven by Brownian motion. We use the techniques of the Malliavin calculus to show that the law of the solution has a density with respect to the Lebesgue measure. We also prove that the density is Holder continuous and satisfies some Gaussian-type estimates. (AU)

• FAPESP's process: 15/07278-0 - Stochastic dynamics: analytical and geometrical aspects with applications
• Grantee: Paulo Regis Caron Ruffino
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 17/17670-0 - Stochastic Partial Differential Equations and Particle Systems
• Grantee: Christian Horacio Olivera
• Support Opportunities: Regular Research Grants