Abstract
We use blow up analysis for local integral equations to provide a blow up rates of solutions of higher order Hardy–Hénon equation in a bounded domain with an isolated singularity, and show the asymptotic radial symmetry of the solutions near the singularity. This work generalizes the correspondence results of Jin–Xiong (in, Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities. arXiv:1901.01678) on higher order conformally invariant equations with an isolated singularity.
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Acknowledgements
We would like to express our deep thanks to Professor Jiguang Bao and Jingang Xiong for useful discussions on the subject of this paper.
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Communicated by Luis Caffarelli.
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Y.M. Li is supported by the Fundamental Research Funds for the Central Universities (No. 2021RC220) and the China Postdoctoral Science Foundation (No. 2020M680324).
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Li, Y. The local behavior of positive solutions for higher order equation with isolated singularities. Calc. Var. 60, 201 (2021). https://doi.org/10.1007/s00526-021-02087-2
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DOI: https://doi.org/10.1007/s00526-021-02087-2