57 citations · 147 across the 13 of their papers we have counts for
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On the heat kernel of the Rumin complex and Calderón reproducing formula
Paolo Ciatti, Bruno Franchi, Yannick Sire
We derive several properties of the heat equation with the Hodge operator associated with the Rumin complex on Heisenberg groups and prove several properties of the fundamental sol…
The role of beta-amyloid and tau proteins in Alzheimer's disease: a mathematical model on graph
Michiel Bertsch, Bruno Franchi, Maria Carla Tesi +1
In this Note we study a mathematical model for the progression of Alzheimer's Disease in the human brain. The novelty of our approach consists in the representation of the brain as…
Well-posedness of a mathematical model for Alzheimer's disease
Michiel Bertsch, Bruno Franchi, Maria Carla Tesi +1
We consider the existence and uniqueness of solutions of an initial-boundary value problem for a coupled system of PDE's arising in a model for Alzheimer's disease. Apart from reac…
Harnack inequality for fractional sub-Laplacians in Carnot groups
Fausto Ferrari, Bruno Franchi
In this paper we prove an invariant Harnack inequality on Carnot-Carathéodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" form…