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- W1566402119 abstract "We study the regularity properties of the solutions to the nonlinear equation with fractional diffusion $$ partial_tu+(-Delta)^{sigma/2}varphi(u)=0, $$ posed for $xin mathbb{R}^N$, $t>0$, with $0 sigma$, and $varphi'(u)>0$ for every $uinmathbb{R}$, 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 $C^infty$ regularity. Degenerate and singular cases, including the power nonlinearity $varphi(u)=|u|^{m-1}u$, $m>0$, are also considered, and the existence of classical solutions in the power case is proved." @default.
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- W1566402119 date "2013-11-28" @default.
- W1566402119 modified "2023-10-09" @default.
- W1566402119 title "Classical solutions and higher regularity for nonlinear fractional diffusion equations" @default.
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