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We study the regularity properties of the solutions to the nonlinear equation with fractional diffusion
posed for , , with , . If the nonlinearity satisfies some not very restrictive conditions: , , and for every , we prove that bounded weak solutions are classical solutions for all positive times. We also explore sufficient conditions on the non-linearity to obtain higher regularity for the solutions, even regularity. Degenerate and singular cases, including the power nonlinearity , , are also considered, and the existence of positive classical solutions until the possible extinction time if , and for all times otherwise, is proved.
Cite this article
Juan Luis Vázquez, Arturo de Pablo, Fernando Quirós, Ana Rodríguez, Classical solutions and higher regularity for nonlinear fractional diffusion equations. J. Eur. Math. Soc. 19 (2017), no. 7, pp. 1949–1975DOI 10.4171/JEMS/710