Seminario del 2022

06/06/2022
09/06/2022
Giacomo Lucertini
Optimal regularity for degenerate Kolmogorov equations with rough coefficients
Seminario di analisi matematica, probabilità
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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