7 citations · 17 across the 13 of their papers we have counts for
16 papers
Harmonic immersions of the Sierpinski gasket into the hyperbolic plane
Ugo Bessi
Many fractals admit a harmonic immersion into , i.e. an immersion which minimises a natural energy under fixed boundary conditions; we look for harmonic immersions of the…
Harmonic embeddings of the stretched Siepinski gasket
Ugo Bessi
P. Alonso-Ruiz, U. Freiberg and J. Kigami have defined a large family of resistance forms on the Stretched Sierpinski Gasket . In the present paper we introduce a system of coor…
Counting periodic orbits on fractals weighted by their Lyapunov exponents
Ugo Bessi
Several authors have shown that Kusuoka's measure on fractals is a scalar Gibbs measure; in particular, it maximises a pressure. There is also a different approach, in which on…
Another point of view on Kusuoka's measure
Ugo Bessi
Kusuoka's measure on fractals is a Gibbs measure of a very special kind, because its potential is discontinuous, while the standard theory of Gibbs measures requires continuous (ac…
Cheeger's energy on the Harmonic Sierpinski Gasket
Ugo Bessi
Koskela and Zhou have proven that, on the harmonic Sierpinski gasket with Kusuoka's measure, the "natural" Dirichlet form coincides with Cheeger's energy. We give a different proof…
Hamilton-Jacobi in metric spaces with a homological term
Ugo Bessi
The Hamilton-Jacobi equation on metric spaces has been studied by several authors; following the approach of Gangbo and Swiech, we show that the final value problem for the Hamilto…
An entropy generation formula on spaces
Ugo Bessi
J. Feng and T. Nguyen have shown that the solutions of the Fokker-Planck equation in satisfy an entropy generation formula. We prove that, in compact metric measure spaces w…
Chaotic motions for a version of the Vlasov equation
Ugo Bessi
We consider a version of the Vlasov equation on the circle under a periodic potential and a repulsing smooth interaction . We suppose that the Lagrangian for the single…
The Aubry set for a version of the Vlasov equation
Ugo Bessi
We check that several properties of the Aubry set, first proven for finite-dimensional Lagrangians by Mather and Fathi, continue to hold in the case of the infinitely many interact…
Viscous Aubry-Mather theory and the Vlasov equation
Ugo Bessi
The Vlasov equation models a group of particles moving under a potential ; moreover, each particle exerts a force, of potential , on the other ones. We shall suppose that the…
A time-step approximation scheme for a viscous version of the Vlasov equation
Ugo Bessi
Gomes and Valdinoci have introduced a time-step approximation scheme for a viscous version of Aubry-Mather theory; this scheme is a variant of that of Jordan, Kinderlehrer and Otto…
The stochastic value function on metric measure spaces
Ugo Bessi
Let be a compact metric space and let be a Borel probability measure on . We shall prove that, if is a space, then the stochastic value…
A cost on paths of measures which induces the Fokker-Planck equation
Ugo Bessi
J. Feng and T. Nguyen have defined a cost on curves of measures which is finite exactly on the curves which solve a Fokker-Planck equation with drift. In this paper, using id…
Existence of solutions of the master equation in the smooth case
Ugo Bessi
We give a different proof of a theorem of W. Gangbo and A. Swiech on the short time existence of solutions of the master equation.
Mañé's conjectures in codimension one
Ugo Bessi, Daniel Massart
We prove Mañé's conjectures in the context of codimension one Aubry-Mather theory
Young measures, Cartesian maps, and polyconvexity
Patrick Bernard, Ugo Bessi
We consider the variational problem consisting of minimizing a polyconvex integrand for maps between manifolds. We offer a simple and direct proof of the existence of a minimizing…