26 citations · 48 across the 30 of their papers we have counts for
4 papers · 1 filter
The fractional Laplacian in power-weighted spaces: integration-by-parts formulas and self-adjointness
Matteo Muratori
We consider the fractional Laplacian operator (let ) on Euclidean space and investigate the validity of the classical integration-by-parts formula that conn…
Weighted interpolation inequalities: a perturbation approach
Jean Dolbeault, Matteo Muratori, Bruno Nazaret
We study optimal functions in a family of Caffarelli-Kohn-Nirenberg inequalities with a power-law weight, in a regime for which standard symmetrization techniques fail. We establis…
Smoothing effects for the porous medium equation on Cartan-Hadamard manifolds
Gabriele Grillo, Matteo Muratori
We prove three sharp bounds for solutions to the porous medium equation posed on Riemannian manifolds, or for weighted versions of such equation. Firstly we prove a smoothing effec…
The porous medium equation with measure data on negatively curved Riemannian manifolds
Gabriele Grillo, Matteo Muratori, Fabio Punzo
We investigate existence and uniqueness of weak solutions of the Cauchy problem for the porous medium equation on negatively curved Riemannian manifolds. We show existence of solut…