Regularity of solutions of a fractional porous medium equation (Q2226679)

The authors study nonnegative solutions of the porous medium equation involving pressure function depending on the density in a nonlinear and nonlocal way considered in [\textit{P. Biler} et al., Arch. Ration. Mech. Anal. 215, No. 2, 497--529 (2015; Zbl 1308.35197)]. The regularity of solutions in the Hölder sense is proved using De Giorgi method together with subtle estimates in the spirit of [\textit{L. Caffarelli} et al., J. Am. Math. Soc. 24, No. 3, 849--869 (2011; Zbl 1223.35098); J. Eur. Math. Soc. (JEMS) 15, No. 5, 1701--1746 (2013; Zbl 1292.35312)], separately in different ranges of the fractional order of Laplacian appearing in the equation.