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Analysis Seminar

Thursday, December 7, 2017 - 3:00pm

Farhan Abedin

Temple University


University of Pennsylvania


I will present some new results on the regularity of solutions to a class of degenerate elliptic and parabolic equations in non-divergence form that possess an underlying Lie group structure. The first half of the talk will be about recent work on Harnack’s inequality for non-divergence form elliptic operators structured on Heisenberg vector fields, with matrix coefficients that are uniformly positive definite, continuous, and symplectic. This is joint work with Cristian Gutierrez (Temple) and Giulio Tralli (University of Rome). In the second half, I will discuss work in progress with Giulio Tralli on non-divergence form parabolic equations of Kolmogorov type.