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Pointwise A Priori Estimates for Solutions to Some p-Laplacian Equations

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Abstract

In this article, we apply blow-up analysis to study pointwise a priori estimates for some p-Laplacian equations based on Liouville type theorems. With newly developed analysis techniques, we first extend the classical results of interior gradient estimates for the harmonic function to that for the p-harmonic function, i.e., the solution of Δpu = 0, x ∈ Ω. We then obtain singularity and decay estimates of the sign-changing solution of Lane-Emden-Fowler type p-Laplacian equation −Δpu = |u|λ − 1u, x ∈ Ω, which are then extended to the equation with general right hand term f(x, u) with certain asymptotic properties. In addition, pointwise estimates for higher order derivatives of the solution to Lane-Emden type p-Laplacian equation, in a case of p = 2, are also discussed.

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Acknowledgements

We acknowledge the editor and anonymous reviewers for their valuable suggestions and comments.

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Authors and Affiliations

  1. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, P. R. China

    Xiao Qiang Sun

  2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, P. R. China

    Ji Guang Bao

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  1. Xiao Qiang Sun
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  2. Ji Guang Bao
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Correspondence to Xiao Qiang Sun.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 11871070 and 62273364), the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020B151502120)

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Sun, X.Q., Bao, J.G. Pointwise A Priori Estimates for Solutions to Some p-Laplacian Equations. Acta. Math. Sin.-English Ser. 38, 2150–2162 (2022). https://doi.org/10.1007/s10114-022-1362-5

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  • DOI: https://doi.org/10.1007/s10114-022-1362-5

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