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

The purpose of this note is to study the relationship between the validity of L1 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 a… (More)

- Yves Achdou, Bruno Franchi, Norina Marcello, Maria Carla Tesi
- Journal of mathematical biology
- 2013

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)

- Bruno Franchi, Maria Carla Tesi
- Math. Comput.
- 2000

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.

- BRUNO FRANCHI, GUOZHEN LU, RICHARD 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, FRANCESCO SERRA CASSANO
- 2006

In the last few years there have been a fairly large amount of work dedicated to the study of intrinsic submanifolds of various dimension and codimension inside the Heisenberg groups H or more general Carnot groups. For example intrinsically C surfaces, rectifiable sets, finite perimeter sets, various notions of convex surfaces have been studied. Here and… (More)

- BRUNO FRANCHI
- 2009

In this paper we prove a Sobolev-Poincaré inequality for a class of function spaces associated with some degenerate elliptic equations. These estimates provide us with the basic tool to prove an invariant Harnack inequality for weak positive solutions. In addition, Holder regularity of the weak solutions follows in a standard way. 1 Let Sf = YJl ,=i… (More)

- Michiel Bertsch, Bruno Franchi, Norina Marcello, Maria Carla Tesi, Andrea Tosin
- Mathematical medicine and biology : a journal of…
- 2017

In this article 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)

- Bruno Franchi, Francesco Serra Cassano
- 2002

We study finite perimeter sets in step 2 Carnot groups. In this way we extend the classical De Giorgi’s theory, developed in Euclidean spaces by De Giorgi, as well as its generalization, considered by the authors, in Heisenberg groups. A structure theorem for sets of finite perimeter and consequently a divergence theorem are obtained. Full proofs of these… (More)

- Yves Achdou, Bruno Franchi, Nicoletta Tchou
- Math. Comput.
- 2005

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)

- Bruno Franchi, Silvia Lorenzani
- J. Nonlinear Science
- 2016