Optimal regularity for degenerate Kolmogorov equations in non-divergence form with rough-in-time coefficients. (English) Zbl 1528.35075
Summary: 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.
MSC:
| 35K65 | Degenerate parabolic equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35A08 | Fundamental solutions to PDEs |
Keywords:
Kolmogorov equations; fundamental solution; Hörmander condition; Hölder estimates; measurable coefficients; parametrix technique; anisotropic diffusionReferences:
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