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Recent Trends in Nonlinear Diffusion

On the Local Behavior of Solutions of Logarithmically Singular Parabolic Equations

speaker: Ugo Gianazza (Dipartimento di Matematica "F. Casorati", Università di Pavia)

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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