On partial regularity of the borderline solution of semilinear parabolic problems

Kai-Seng Chou; Shi-Zhong Du; Gao-Feng Zheng
October 2007
Calculus of Variations & Partial Differential Equations;Oct2007, Vol. 30 Issue 2, p251
Academic Journal
The global, weak solutions for the semilinear problem (1) introduced in Ni-Sacks-Tavantzis (J. Differ. Eq. 54, 97�120 (1984)) are studied. Estimates on the Hausdorff dimension of their singular sets are found. As an application, it is shown that these solutions must blow up in finite time and become regular eventually when the nonlinearity is supercritical and the domain is convex.


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