4 papers · 1 filter
On the subcritical Lane-Emden equation on Riemannian models with polynomial volume growth
Alessandra De Luca, Matteo Muratori, Nicola Soave
We focus on the problems of existence and non-existence of positive solutions for the Sobolev-subcritical Lane-Emden equation on certain Riemannian manifolds (mainly models) with a…
A general nonlinear characterization of stochastic incompleteness
Gabriele Grillo, Kazuhiro Ishige, Matteo Muratori +1
Stochastic incompleteness of a Riemannian manifold amounts to the nonconservation of probability for the heat semigroup on . We show that this property is equivalent to the…
Concentration comparison for nonlinear diffusion on model manifolds and Pólya-SzegŠinequality
Matteo Muratori, Bruno Volzone
We investigate the validity of the mass concentration comparison for a class of nonlinear diffusion equations posed on Riemannian manifolds that are spherically sy…
A porous medium equation with rough weights: sharp Widder theory
Gabriele Grillo, Matteo Muratori, Troy Petitt +1
We establish an optimal \emph{Widder theory} for a weighted porous medium equation with rough and inhomogeneous density that may be singular at a point and tends to zero at spatial…