**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.

Mon 2 Jul, 11:25 - 12:25, Aula Dini

Gianazza 2nd July

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