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arXiv · 2204.14158

Optimal regularity for degenerate Kolmogorov equations with rough coefficients

Giacomo Lucertini·Stefano Pagliarani·Andrea Pascucci
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Abstract

We consider a class of degenerate equations satisfying a parabolic H\"ormander condition, with coefficients that are measurable in time and H\"older continuous in the space variables. By utilizing a generalized notion of strong solution, we establish the existence of a fundamental solution and its optimal H\"older 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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Giacomo Lucertini, Stefano Pagliarani, Andrea Pascucci. 2022-04-29. Optimal regularity for degenerate Kolmogorov equations with rough coefficients. https://arxiv.org/abs/2204.14158

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