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Bianchi, Davide; Setti, Alberto G.
Calculus of variations and partial differential equations, 02/2018, Letnik: 57, Številka: 1Journal Article
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 L q -properties of the gradient and of the self-adjointness of Schrödinger-type operators.
