17 articles in this issue
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