Research Interests

Degenerate nonlinear PDEs under the Hörmander condition
My main research area are nonlinear partial differential equations under the Hoermander condition (also called subellipticity). These kind of equations describe many phenomena in science and economics and are characterized by a condition named after Lars Hoermander, which is a condition on the geometry associated to the equation. In fact, one can introduce a geometric structure associated to a partial differential equation in the following way: Partial derivatives can be interpreted as derivatives along the basis directions of the Euclidean space. In the Hoermander case, the Euclidean basis is replaced by a family of vector fields which span a space with dimension smaller than the dimension of the ambient space (therefore degenerate). Nevertheless these vector fields are such that some differential operations (called commutators) still allow to move in all directions. In other words, the commutators generate a space of full dimension. Hence the partial derivatives are interpreted as derivatives along the vector fields which replace the Euclidean basis.

Research Group

Analysis

Recent Significant Publications

F. Dragoni, J.J. Manfredi and D. Vittone: Weak Fubini property and infinity harmonic functions in Riemannian and Sub-Riemannian manifolds. Accepted, Trans. Amer. Math. Soc

M. Bardi and F. Dragoni: Convexity and Semiconvexity along Vector Fields. Accepted, Calc. Var. Partial Differential Equations.

N. Dirr, F. Dragoni, and M. v. Renesse Evolution by mean curvature flow in sub-Riemannian geometries: a stochastic approach.Communications on Pure and Applied Analysis 9, no. 2, (2010), pp. 307-326

T. Bieske, F. Dragoni, J.J. Manfredi: The Carnot-Caratheodory distance and the infinite Laplacian. Journal of Geometric Analysis 19, N. 4 (2009), 737-754

Personal Website

Dr Federica Dragoni's Personal Website.