25 citations · 95 across the 28 of their papers we have counts for
22 papers · 1 filter
The fractional Porous Medium Equation on graphs
Elvise Berchio, Federico Santagati, Maria Vallarino
We study the fractional porous medium equation on connected infinite graphs with no local finiteness assumption. We introduce a notion of weak dual solution adapted to the discrete…
Semilinear Diffusion Equations on Infinite Graphs: The Dissipative and Lipschitz Cases
Elvise Berchio, Davide Bianchi, Alberto G. Setti +1
We study a class of semilinear diffusion equations on infinite, connected, weighted graphs, focusing on two types of nonlinearities: monotone decreasing and Lipschitz continuous. U…
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…
Classification of radial solutions to on Riemannian models
Elvise Berchio, Alberto Ferrero, Debdip Ganguly +1
We provide a complete classification with respect to asymptotic behaviour, stability and intersections properties of radial smooth solutions to the equation on Riemann…
The Fractional Porous Medium Equation on noncompact Riemannian manifolds
Elvise Berchio, Matteo Bonforte, Gabriele Grillo +1
We study nonnegative solutions to the Fractional Porous Medium Equation on a suitable class of connected, noncompact Riemannian manifolds. We provide existence and smoothing estima…
Hardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs
Elvise Berchio, Debdip Ganguly, Prasun Roychowdhury
We prove a family of Hardy-Rellich and Poincaré identities and inequalities on the hyperbolic space having, as particular cases, improved Hardy-Rellich, Rellich and second order Po…