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- Bruno Franchi, Raul Serapioni, Francesco Serra Cassano
- 2004

We describe intrinsically regular submanifolds in Heisen-berg groups H n. Low dimensional and low codimensional submanifolds turn out to be of a very different nature. The first ones are Legendrian surfaces, while low codimensional ones are more general objects, possibly non Euclidean rectifiable. Nevertheless we prove that they are graphs in a natural… (More)

- Bruno Franchi, Guozhen Lu, Richard L Wheeden
- 1995

The purpose of this note is to study the relationship between the validity of L 1 versions of Poincaré's inequality and the existence of representation formulas for functions as (fractional) integral transforms of first-order vector fields. The simplest example of a representation formula of the type we have in mind is the following familiar inequality for… (More)

- Bruno Franchi, Guozhen Lu, Richard L Wheeden, B Franchi, G Lu, R L Wheeden
- 2003

tion commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit conte-nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques

- Bruno Franchi, Raul Serapioni
- 2006

In this paper we exhibit a finite element method fitting a suitable geometry naturally associated with a class of degenerate elliptic equations (usually called Grushin type equations) in a plane region, and we discuss the related error estimates.

- Michiel Bertsch, Bruno Franchi, Norina Marcello, Maria Carla Tesi, Andrea Tosin
- 2015

In this paper we propose a mathematical model for the onset and progression of Alzheimer's disease based on transport and diffusion equations. We regard brain neurons as a continuous medium, and structure them by their degree of malfunctioning. Two different mechanisms are assumed to be relevant for the temporal evolution of the disease: i) diffusion and… (More)

In this paper we present a mathematical model for the aggregation and diffusion of Aβ amyloid in the brain affected by Alzheimer's disease, at the early stage of the disease. The model is based on a classical discrete Smoluchowski aggregation equation modified to take diffusion into account. We also describe a numerical scheme and discuss the results of the… (More)

This paper completes a previous work on a Black and Scholes equation with stochastic volatility. This is a degenerate parabolic equation, which gives the price of a European option as a function of the time, of the price of the underlying asset, and of the volatility, when the volatility is a function of a mean reverting Orstein–Uhlenbeck process, possibly… (More)

- Annalisa Baldi, Bruno Franchi, Nicoletta Tchou
- 2008

In this paper we prove a compensated compactness theorem for differential forms of the intrinsic complex of a Carnot group. The proof relies on a L s –Hodge decomposition for these forms. Because of the lack of homogeneity of the intrinsic exterior differential, Hodge decomposition is proved using the parametrix of a suitable 0-order Laplacian on forms.