A sufficient condition for the continuity of solutions to a logarithmic diffusion equation

2017/03/18 by Liao, Naian
#35B65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35K67 #Secondary 35B45

paper · doi:10.48550/arxiv.1703.06248

Abstract

This note gives a first sufficient condition that insures a non-negative, locally bounded, local solution to a logarithmically singular parabolic equation is continuous at a vanishing point and an estimate of the modulus of continuity is given. Moreover, an estimate of the Hausdorff measure of the set of discontinuity is established.

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