Estimates for the distances between solutions to Kolmogorov equations with diffusion matrices of low regularity

Communications on Pure &amp Applied Analysis 2026 Open access

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Authors: Vladimir Igorevich Bogachev, Stanislav Valer'evich Shaposhnikov
DOI: 10.3934/cpaa.2026064
Cited by: 0

Abstract

We obtain estimates for the weighted $L^1$-norm of the difference of two probability solutions to Kolmogorov equations in terms of the difference of the diffusion matrices and the drifts. Unlike the previously known results, our estimate does not involve Sobolev derivatives of solutions and coefficients. The diffusion matrices are supposed to be non-singular, bounded and satisfy the Dini mean oscillation condition.

Fields of Study & Subjects

Stochastic processes and financial applications Nonlinear Differential Equations Analysis Spectral Theory in Mathematical Physics

Publication details

Journal / source
Communications on Pure &amp Applied Analysis
Volume
35
Issue
0
Pages
48–60
Publication date
1 January 2026