3 papers
math.AP2017
Porous medium equations on manifolds with critical negative curvature: unbounded initial data
Matteo Muratori, Fabio Punzo
We investigate existence and uniqueness of solutions of the Cauchy problem for the porous medium equation on a class of Cartan-Hadamard manifolds. We suppose that the radial Ricci…
math.AP2016
Symmetry for extremal functions in subcritical Caffarelli-Kohn-Nirenberg inequalities
Jean Dolbeault, Maria J. Esteban, Michael Loss +1
We use the formalism of the R{é}nyi entropies to establish the symmetry range of extremal functions in a family of subcriti-cal Caffarelli-Kohn-Nirenberg inequalities. By extremal…
math.AP2016
The porous medium equation on Riemannian manifolds with negative curvature. The large-time behaviour
Gabriele Grillo, Matteo Muratori, Juan Luis Vázquez
We consider nonnegative solutions of the porous medium equation (PME) on a Cartan-Hadamard manifold whose negative curvature can be unbounded. We take compactly supported initial d…