175 citations · 580 across the 34 of their papers we have counts for
40 papers
The Pohozaev identity for the Spectral Fractional Laplacian
Itahisa Barrios-Cubas, Matteo Bonforte, María del Mar González +1
In this paper, we prove a Pohozaev identity for the Spectral Fractional Laplacian (SFL). This identity allows us to establish non-existence results for the semilinear Dirichlet pro…
Sharp Boundary Estimates and Harnack Inequalities for Fractional Porous Medium type Equations
Matteo Bonforte, Carlos Fuertes-Moran
This paper provides sharp quantitative and constructive estimates of nonnegative solutions to the nonlinear fractional diffusion equation, $$\partial_t u +{\mathcal…
Is Stochastic Gradient Descent Effective? A PDE Perspective on Machine Learning processes
Davide Barbieri, Matteo Bonforte, Peio Ibarrondo
In this paper we analyze the behaviour of the stochastic gradient descent (SGD), a widely used method in supervised learning for optimizing neural network weights via a minimizatio…
Asymptotic behavior of a diffused interface volume-preserving mean curvature flow
Matteo Bonforte, Francesco Maggi, Daniel Restrepo
We consider a diffused interface version of the volume-preserving mean curvature flow in the Euclidean space, and prove, in every dimension and under natural assumptions on the ini…
Smoothing effects and extinction in finite time for fractional fast diffusions on Riemannian manifolds
Elvise Berchio, Matteo Bonforte, Gabriele Grillo
We study nonnegative solutions to the Cauchy problem for the Fractional Fast Diffusion Equation on a suitable class of connected, noncompact Riemannian manifolds. This parabolic eq…
Refined asymptotics for the Cauchy problem for the fast -Laplace evolution equation
Matteo Bonforte, Iwona Chlebicka, Nikita Simonov
Our focus is on the fast diffusion equation driven by the -Laplacian operator, that is with , posed in the whole space , . The…