Laplacian cut-offs, porous and fast diffusion on manifolds and other applications

By D. Bianchi, A. G. Setti. 2016

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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 $$L^q$$Lq-properties of the gradient and of the self-adjointness of Schrödinger-type operators.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/938357e11742f9e1a3bfdfe83b1f22ee7d0c77db