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math.DG2008
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…
math.DG2008★ 14 cited
Sharp logarithmic Sobolev inequalities on gradient solitons and applications
Jose Carrillo, Lei Ni
We show that gradient shrinking, expanding or steady Ricci solitons have potentials leading to suitable reference probability measures on the manifold. For shrinking solitons, as w…