17 citations · 29 across the 4 of their papers we have counts for
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Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds
Peng Lu, Lei Ni, Juan-Luis Vázquez +1
In this work we derive local gradient and Laplacian estimates of the Aronson-Bénilan and Li-Yau type for positive solutions of porous medium equations posed on Riemannian manifolds…
The Hamilton-Jacobi semigroup on length spaces and applications
John Lott, Cedric Villani
We define a Hamilton-Jacobi semigroup acting on continuous functions on a compact length space. Following a strategy of Bobkov, Gentil and Ledoux, we use some basic properties of t…
Weak curvature conditions and functional inequalities
John Lott, Cedric Villani
We give sufficient conditions for a measured length space (X,d,m) to admit local and global Poincare inequalities. We first introduce a condition DM on (X,d,m), defined in terms of…
Ricci curvature for metric-measure spaces via optimal transport
John Lott, Cedric Villani
We define a notion of a measured length space X having nonnegative N-Ricci curvature, for N finite, or having infinity-Ricci curvature bounded below by K, for K a real number. The…