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.
2018
http://link.springer-ny.com/link/service/journals/00526/index.htm
35K55; 53C21; 58J35; 58J65; Analysis; Applied Mathematics
Bianchi, Davide; Setti, Alberto G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2068461
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