UGO GIANAZZA's LATEST PREPRINTS

[1] E. DiBenedetto, U. Gianazza and N. Liao - On the Local Behavior of Non-Negative Solutions to a Logarithmically Singular Equation - preprint (2011), 1-21, to appear in Discrete Contin. Dyn. Syst. Ser. B.
Abstract: The local positivity of solutions to logarithmically singular diffusion equations is investigated in some open space-time domain $E\times(0,T]$. It is shown that if at some time level $t_o\in(0,T]$ and some point $x_o\in E\,$ the solution $u(\cdot,t_o)$ is not identically zero in a neighborhood of $x_o$, in a measure-theoretical sense, then it is strictly positive in a neighborhood of $(x_o,t_o)$. The precise form of this statement is by an intrinsic Harnack-type inequality, which also determines the size of such a neighborhood.