Density estimates for differential equations of second order satisfying a weak Hoermander condition

2013/07/20 by Joerg Kampen, Kampen, Joerg
Computer Science · Engineering · Mathematics · #35A08 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Controllability of Differential Equations #math.AP #math.PR #msc:35A08

paper · pdf · doi:10.48550/arxiv.1307.5399

30p

arxiv created 2013/07/20 · openalex publication_date 2013/07/20 · arxiv updated 2013/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an extension of Hoermander's classical result on hypoelliptic second order equations, where the coefficients of the related vector fields are globally Lipschitz and satisfy the classical Hoermander condition on a dense set while the density still exists in a classical sense. Furthermore, Hoermander's classical result and related density estimates based on Malliavin calculus are recovered from an analytical point of view.

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