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On partial regularity of the borderline solution of semilinear parabolic problems

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong

    Kai-Seng Chou & Shi-Zhong Du

  2. Department of Mathematics, Huazhong Normal University, Wuhan, 430079, Peoples Republic of China

    Gao-Feng Zheng

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  1. Kai-Seng Chou
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  2. Shi-Zhong Du
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  3. Gao-Feng Zheng
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Correspondence to Kai-Seng Chou.

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Chou, KS., Du, SZ. & Zheng, GF. On partial regularity of the borderline solution of semilinear parabolic problems. Calc. Var. 30, 251–275 (2007). https://doi.org/10.1007/s00526-007-0093-x

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  • DOI: https://doi.org/10.1007/s00526-007-0093-x

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