We prove optimal regularity for solutions to porous media equations in Sobolev spaces, based on velocity averaging techniques. In particular, the regularity obtained is consistent with the optimal regularity in the linear limit.
Cite this article
Benjamin Gess, Optimal regularity for the porous medium equation. J. Eur. Math. Soc. 23 (2021), no. 2, pp. 425–465DOI 10.4171/JEMS/1014