7 papers
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…
On the accretivity and m-accretivity of Laplacians and porous medium-type operators on graphs
Davide Bianchi, Matthias Keller, Alberto G. Setti +2
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…
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…
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…