Optimal regularity for degenerate Kolmogorov equations with rough coefficients

2022/04/29 by Giacomo Lucertini, Lucertini, Giacomo, Stefano Pagliarani +3
Economics, Econometrics and Finance · Engineering · Mathematics · #35B65 #35D99 #35K65 #60J60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2204.14158

openalex publication_date 2022/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a class of degenerate equations satisfying a parabolic Hörmander condition, with coefficients that are measurable in time and Hölder continuous in the space variables. By utilizing a generalized notion of strong solution, we establish the existence of a fundamental solution and its optimal Hölder regularity, as well as Gaussian estimates. These results are key to study the backward Kolmogorov equations associated to a class of Langevin-type diffusions.

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