[CvGmt News] [cvgmt seminar] Hörmander operators in nondivergence form: a Landis-type approach

luciano.mari at sns.it luciano.mari at sns.it
Tue Nov 6 10:13:49 CET 2018

Hörmander operators in nondivergence form: a  Landis-type approach


Date: Thursday, Nov  8, 2018

Time: 14:00

Place: Scuola Normale Superiore, aula Bianchi Scienze

Speaker: Giulio Tralli

Abstract. In this talk we will discuss the validity of Harnack inequalities for linear degenerate-elliptic equations of
Hörmander type with non-smooth coefficients. We are interested in operators in nondivergence form, for
which the analogous of the Krylov-Safonov Harnack inequality for equations with bounded measurable
coefficients is still unknown. We will show a perturbative approach to prove invariant Harnack
inequalities for operators with coefficients satisfying either a Cordes-Landis assumption or a continuity hypothesis. We will consider two specific classes of equations: the first class is formed by degenerate-
elliptic operators which are horizontally elliptic with respect to Heisenberg-type vector fields; the second one constitutes a class of evolution operators of Kolmogorov-Fokker-Planck type. This talk is mainly based on joint works with F. Abedin and C.E. Gutiérrez.

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