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.
Gianazza 2nd July