76 citations · 172 across the 24 of their papers we have counts for
29 papers
On the accretivity and m-accretivity of Laplacians and porous medium-type operators on graphs
Davide Bianchi, Matthias Keller, Alberto G. Setti +1
We study the accretivity and m-accretivity of Laplacian and porous medium-type operators on weighted graphs. In particular, we give several conditions that imply these properties f…
Nonlinear parabolic characterizations of stochastic completeness at infinity on weighted graphs
Davide Bianchi, Bobo Hua, Alberto G. Setti +1
We prove a nonlinear parabolic characterization of stochastic completeness at infinity for weighted graphs. For the filtration equation \[ (\partial_t + ΔΦ)u =0 \] where is the…
The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation
Davide Bianchi, Bobo Hua, Alberto G. Setti +1
We study the Cauchy problem for the generalized porous medium equation on infinite weighted graphs. For a general nonlinearity, we establish Dirichlet comparison and weak maximum p…
Proper solutions of the -flow and the Green kernel of the -Laplacian
Luca Benatti, Luciano Mari, Marco Rigoli +2
We show existence and optimal growth estimate for the weak inverse mean curvature flow issuing from a point, on manifolds with certain curvature and isoperimetric conditions. These…
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…
Characterizations of -Parabolicity on Graphs
Andrea Adriani, Florian Fischer, Alberto G. Setti
We study -energy functionals on infinite locally summable graphs for and show that many well-known characterizations for a parabolic space are also true in thi…