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On singular sets of local solutions to p-Laplace equations

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Abstract

The author proves that the right-hand term of a p-Laplace equation is zero on the singular set of a local solution to the equation. Such a result is used to study the existence of an optimal control problem.

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Authors and Affiliations

  1. Key Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Hongwei Lou

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  1. Hongwei Lou
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Correspondence to Hongwei Lou.

Additional information

Project supported by the National Natural Science Foundation of China (No. 10671040), the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 200522) and the Program for New Century Excellent Talents in University of China (No. 06-0359).

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Lou, H. On singular sets of local solutions to p-Laplace equations. Chin. Ann. Math. Ser. B 29, 521–530 (2008). https://doi.org/10.1007/s11401-007-0312-y

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  • DOI: https://doi.org/10.1007/s11401-007-0312-y

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