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- W2051391036 abstract "We investigate local and global properties of positive solutions to the fast diffusion equation in the good exponent range , corresponding to general nonnegative initial data. For the Cauchy problem posed in the whole Euclidean space , we prove sharp local positivity estimates (weak Harnack inequalities) and elliptic Harnack inequalities; also a slight improvement of the intrinsic Harnack inequality is given. We use them to derive sharp global positivity estimates and a global Harnack principle. Consequences of these latter estimates in terms of fine asymptotics are shown. For the mixed initial and boundary value problem posed in a bounded domain of with homogeneous Dirichlet condition, we prove weak, intrinsic, and elliptic Harnack inequalities for intermediate times. We also prove elliptic Harnack inequalities near the extinction time, as a consequence of the study of the fine asymptotic behavior near the finite extinction time." @default.
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- W2051391036 date "2007-01-01" @default.
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- W2051391036 title "Reverse Smoothing Effects, Fine Asymptotics, and Harnack Inequalities for Fast Diffusion Equations" @default.
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- W2051391036 doi "https://doi.org/10.1155/2007/21425" @default.
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