Le Matematiche  

Marco Bramanti

This is a survey paper about the proof of the hypoellipticity theorem by Hörmander (Acta Math. 1967). We will compare three different proofs of this result: the original one by Hörmander, the proof given by Kohn (Proc. Sympos. Pure Math., 1973) and indepe... see more

Antonino Morassi, Edi Rosset, Sergio Vessella

The main result of this paper is a doubling inequality at the boundary for solutions to the Kirchhoff-Love isotropic plate's equation satisfying homogeneous Dirichlet conditions. This result, like the three sphere inequality with optimal exponent at the b... see more

Giovanni Alessandrini, Vincenzo Nesi

We consider mappings U=(u1,u2), whose components solve an arbitrary elliptic equation in divergence form in dimension two, and whose respective Dirichlet data f1,f2 constitute the parametrization of a simple closed curve ?. We prove that, if the inte... see more

Andrea Bonfiglioli

Let X = {X1, ... ,Xm} be a set of Hörmander vector fields in Rn, where any Xj is homogeneous of degree 1 with respect to a family of non-isotropic dilations in Rn. If N is the dimension of Lie{X}, we can either lift X to a system of generators of a&n... see more

Roberto Monti, Michele Zaccaron

We prove a height estimate and an approximation with Lipschitz graphs for geodesics in Carnot groups in the small excess regime

Salvatore A. Marano, Sunra Mosconi

The general stability problem of truncations for a family of functions concentrating mass at the origin is described and a concrete example in the framework of entire optimizers for the fractional Hardy-Sobolev inequality is given. In this short note we p... see more

Giulio Tralli, Francesco Uguzzoni

In this note we review some recent results in [64, 95, 96] concerning necessary and sufficient conditions for the regularity of boundary points relatively to the Dirichlet problem for linear degenerate-parabolic operators with well-behaved fundamental sol... see more

Pier Domenico Lamberti, Luigi Provenzano

We survey a few trace theorems for Sobolev spaces on N-dimensional Euclidean domains. We include known results on linear subspaces, in particular hyperspaces, and smooth boundaries, as well as less known results for Lipschitz boundaries, including Besov's... see more

Annalisa Baldi, Bruno Franchi, Pierre Pansu

In this paper we prove Poincar´e and Sobolev inequalities for differential forms in the Rumin’s contact complex on Heisenberg groups. In particular, we deal with endpoint values of the exponents, obtaining finally estimates akin to exponent... see more

Giampiero Palatucci, Simone Vincini

We study the asymptotic behavior as e goes to 0 of an appropriate scaling of the following nonlocal Allen-Cahn energy,where I is an interval in R, and W is a double-well potential. We provide a G-convergence result for any s ? (0,... see more

Francesca Anceschi, Sergio Polidoro

We present a survey on the regularity theory for classic solutions to subelliptic degenerate Kolmogorov equations. In the last part of this note we present a detailed proof of a Harnack inequality and a strong maximum principle.

Dario Daniele Monticelli, Scott Rodney

This short note investigates the compact embedding of degenerate matrix weighted Sobolev spaces into weighted Lebesgue spaces. The Sobolev spaces explored are defined as the abstract completion of Lipschitz functions in a bounded domain ? with respect to ... see more

Simona Fornaro, Eurica Henriques, Vincenzo Vespri

In this note, we concern with a class of doubly nonlinear operators whose prototype isut - div(|u|m-1|Du|p-2Du) = 0,        p > 1,         m + p = 2.In the last few years many progresses were made in understandin... see more

Annamaria Montanari, Daniele Morbidelli

We discuss some estimates of subelliptic type related with vector fields satisfying the Hormander condition. Our approach makes use of a class of approximate exponentials studied in our previous papers. Such kind of estimates arises naturally in... see more

Giovanni Cupini, Ermanno Lanconelli

The Euclidean ball have the following harmonic characterization, via Gauss-mean value property: Let D be an open set with finite Lebesgue measure and let x0 be a point of D. If for every nonnegative harmonic function u in D, then D is a Euc... see more

Emanuele Spadaro

A mean-convex set is locally a barrier for minimal surfaces but can fail to be a global barrier. In this note we suggest how to extend to general dimensions the results of a previous unpublished manuscript on the characterization of the global barrie... see more

Francesco Serra Cassano, Mattia Vedovato

In these notes, we collect the main and, to the best of our knowledge, most up-to-date achievements concerning the Bernstein problem in the Heisenberg group; that is, the problem of determining whether the only entire minimal graphs are hyperplanes. We an... see more