Giovanna Citti, Regularity of solutions of prescribed Levi curvature equation

I'll recall some regularity results for solutions of the prescribed Levi curvature equation, which naturally arises while studying properties of pseudoconvex domains in C^2. We will restrict to the curvature of graphs, which can be written as a sum of squares of non linear vector fields. The commutators of the vector fields is expressed in terms of the Levi curvature, and local approximation via Lie groups allows to establish internal regularity result. These results have been obtained some years ago, in collaboration with Lanconelli and Montanari. Regularity at the boundary is still an open problem: we only have by now a preliminar result for linear equation, obtained in collaboration with G. Giovannardi and Y Sire.