On the Local Behavior of Non-negative Solutions to a Logarithmically Singular Equation
نویسنده
چکیده
The local positivity of solutions to logarithmically singular diffusion equations is investigated in some space-time domain E×(0, T ]. It is shown that if at some time level to ∈ (0, T ] and some point xo ∈ E the solution u(·, to) is not identically zero in a neighborhood of xo, in a measure-theoretical sense, then it is strictly positive in a neighborhood of (xo, to). The precise form of this statement is by an intrinsic Harnack-type inequality, which also determines the size of such a neighborhood. Further results on L-type Harnack estimates and analyticity of solutions are presented.
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