89 citations · 178 across the 9 of their papers we have counts for
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Hamilton--Jacobi equations for controlled gradient flows: cylindrical test functions
Giovanni Conforti, Richard C. Kraaij, Daniela Tonon
This work is the second part of a program initiated in arXiv:2111.13258 aiming at the development of an intrinsic geometric well-posedness theory for Hamilton-Jacobi equations rela…
Hamilton--Jacobi equations for controlled gradient flows: the comparison principle
Giovanni Conforti, Richard Kraaij, Daniela Tonon
Motivated by recent developments in the fields of large deviations for interacting particle system and mean field control, we establish a comparison principle for the Hamilton--Jac…
The planning problem in Mean Field Games as regularized mass transport
P. Jameson Graber, Alpár R. Mészáros, Francisco J. Silva +1
In this paper, using variational approaches, we investigate the first order planning problem arising in the theory of mean field games. We show the existence and uniqueness of weak…
Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off
Frédéric Hérau, Daniela Tonon, Isabelle Tristani
In this paper, we investigate the problems of Cauchy theory and exponential stability for the inhomogeneous Boltzmann equation without angular cut-off. We only deal with the physic…
Short time diffusion properties of inhomogeneous kinetic equations with fractional collision kernel
Frédéric Hérau, Daniela Tonon, Isabelle Tristani
We prove regularization properties in short time for inhomogeneous kinetic equations whose collision kernel behaves like a fractional power of the Laplacian in velocity. We treat a…
Time-dependent focusing Mean-Field Games: the sub-critical case
Marco Cirant, Daniela Tonon
We consider time-dependent viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in mean-field game theory, and describe Nas…
Sobolev regularity for the first order Hamilton-Jacobi equation
Pierre Cardaliaguet, Alessio Porretta, Daniela Tonon
We provide Sobolev estimates for solutions of first order Hamilton-Jacobi equations with Hamiltonians which are superlinear in the gradient variable. We also show that the solution…
BV-regularity of the Boltzmann equation in Non-Convex Domains
Yan Guo, Chanwoo Kim, Daniela Tonon +1
Consider the Boltzmann equation in a general non-convex domain with the diffuse boundary condition. We establish optimal BV estimates for such solutions. Our method consists of a n…
Regularity of the Boltzmann Equation in Convex Domains
Yan Guo, Chanwoo Kim, Daniela Tonon +1
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the n…