Optimal regularity for degenerate Kolmogorov equations in non-divergence form with rough-in-time coefficients

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2023-10-26 DOI:10.1007/s00028-023-00916-9

Stefano Pagliarani, Giacomo Lucertini, Andrea Pascucci

引用次数: 2

Abstract

Abstract We consider a class of degenerate equations in non-divergence form 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 diffusions.

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具有粗糙时间系数的非散度形式退化Kolmogorov方程的最优正则性

摘要考虑一类满足抛物型Hörmander条件的退化方程，其系数在时间上可测，在空间变量上Hölder连续。利用广义强解的概念，我们建立了一个基本解的存在性及其最优Hölder正则性，以及高斯估计。这些结果是研究一类朗格万扩散的后向Kolmogorov方程的关键。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators