Journal of the European Mathematical Society


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Volume 15, Issue 5, 2013, pp. 1701–1746
DOI: 10.4171/JEMS/401

Published online: 2013-07-21

Regularity of solutions of the fractional porous medium flow

Luis A. Caffarelli[1], Fernando Soria[2] and Juan Luis Vázquez[3]

(1) University of Texas at Austin, USA
(2) Universidad Autónoma de Madrid, Spain
(3) Universidad Autónoma de Madrid, Spain

We study a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. The precise model is $$u_t=\nabla\cdot(u\nabla (-\Delta)^{-s}u), \quad \ 0

Keywords: Porous medium equation, fractional Laplacian, nonlocal operator, regularity

Caffarelli Luis, Soria Fernando, Vázquez Juan Luis: Regularity of solutions of the fractional porous medium flow. J. Eur. Math. Soc. 15 (2013), 1701-1746. doi: 10.4171/JEMS/401