We construct exhaustion and cut-off functions with controlled gradient and Laplacian on manifolds with Ricci curvature bounded from below by a (possibly unbounded) nonpositive function of the distance from a fixed reference point, without any assumptions on the topology or the injectivity radius. Along the way we prove a generalization of the Li-Yau gradient estimate which is of independent interest. We then apply our cut-offs to the study of the fast and porous media diffusion, of Lq-properties of the gradient and of the self-adjointness of Schrödinger-type operators.
Laplacian cut-offs, porous and fast diffusion on manifolds and other applications
Bianchi, Davide;Setti, Alberto G.
2018-01-01
Abstract
We construct exhaustion and cut-off functions with controlled gradient and Laplacian on manifolds with Ricci curvature bounded from below by a (possibly unbounded) nonpositive function of the distance from a fixed reference point, without any assumptions on the topology or the injectivity radius. Along the way we prove a generalization of the Li-Yau gradient estimate which is of independent interest. We then apply our cut-offs to the study of the fast and porous media diffusion, of Lq-properties of the gradient and of the self-adjointness of Schrödinger-type operators.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.