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Asymptotic behavior of solutions of Schrödinger inequalities on unbounded domains of nilpotent Lie groups

Francesco Uguzzoni — 1999

Rendiconti del Seminario Matematico della Università di Padova

Degree theory for VMO maps on metric spaces

Francesco Uguzzoni; Ermanno Lanconelli — 2002

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We construct a degree theory for Vanishing Mean Oscillation functions in metric spaces, following some ideas of Brezis & Nirenberg. The underlying sets of our metric spaces are bounded open subsets of $ℝ^{N}$ and their boundaries. Then, we apply our results in order to analyze the surjectivity properties of the $L$ -harmonic extensions of VMO vector-valued functions. The operators $L$ we are dealing with are second order linear differential operators sum of squares of vector fields satisfying the hypoellipticity...

A note on lifting of Carnot groups.

Andrea Bonfiglioli; Francesco Uguzzoni — 2005

Revista Matemática Iberoamericana

We prove that every homogeneous Carnot group can be lifted to a free homogeneous Carnot group. Though following the ideas of Rothschild and Stein, we give simple and self-contained arguments, providing a constructive proof, as shown in the examples.

Levi's parametrix for some sub-elliptic non-divergence form operators.

Bonfiglioli, Andrea; Lanconelli, Ermanno; Uguzzoni, Francesco — 2003

Electronic Research Announcements of the American Mathematical Society [electronic only]

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