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Gaussian lower bounds for non-homogeneous Kolmogorov equations with measurable coefficients

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Abstract

We prove Gaussian upper and lower bounds for the fundamental solutions of a class of degenerate parabolic equations satisfying a weak Hörmander condition. The bound is independent of the smoothness of the coefficients and generalizes classical results for uniformly parabolic equations.

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Acknowledgements

Sergio Polidoro gratefully acknowledges the financial support by INDAM-GNAMPA.

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Authors and Affiliations

  1. Dipartimento di Scienze Statistiche “Paolo Fortunati”, Università di Bologna, Bologna, Italy

    Alberto Lanconelli

  2. Dipartimento di Matematica, Università di Bologna, Bologna, Italy

    Andrea Pascucci

  3. Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Modena, Italy

    Sergio Polidoro

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  1. Alberto Lanconelli
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  2. Andrea Pascucci
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  3. Sergio Polidoro
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Correspondence to Alberto Lanconelli.

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Lanconelli, A., Pascucci, A. & Polidoro, S. Gaussian lower bounds for non-homogeneous Kolmogorov equations with measurable coefficients. J. Evol. Equ. 20, 1399–1417 (2020). https://doi.org/10.1007/s00028-020-00560-7

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