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math.AP2020
Fast diffusion on noncompact manifolds: well-posedness theory and connections with semilinear elliptic equations
Gabriele Grillo, Matteo Muratori, Fabio Punzo
We investigate the well-posedness of the fast diffusion equation (FDE) in a wide class of noncompact Riemannian manifolds. Existence and uniqueness of solutions for globally integr…
math.AP2020★ 1 cited
Nonexistence of radial optimal functions for the Sobolev inequality on Cartan-Hadamard manifolds
Tatsuki Kawakami, Matteo Muratori
It is well known that the Euclidean Sobolev inequality holds on any Cartan-Hadamard manifold of dimension , i.e. any complete, simply connected Riemannian manifold with n…