Calculus of Variations and Geometric Measure Theory

Hörmander operators in nondivergence form: a Landis-type approach

Giulio Tralli

created by mari1 on 06 Nov 2018

8 nov 2018 -- 14:00   [open in google calendar]

Scuola Normale Superiore, aula Bianchi Scienze


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.