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arXiv · 1607.06008

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

Davide Bianchi·Alberto G. Setti
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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 $L^q$-properties of the gradient and of the self-adjointness of Schroedinger-type operators.

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Davide Bianchi, Alberto G. Setti. 2016-07-20. Laplacian cut-offs, porous and fast diffusion on manifolds and other applications. https://doi.org/10.1007/s00526-017-1267-9

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