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Strong unique continuation property for a class of fourth order elliptic equations with strongly singular potentials

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Abstract

In this paper we prove the strong unique continuation property for a class of fourth order elliptic equations involving strongly singular potentials. Our argument is to establish some Hardy-Rellich type inequalities with boundary terms and introduce an Almgren’s type frequency function to show some doubling conditions for the solutions to the above-mentioned equations.

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Acknowledgements

The first author was supported by National Natural Science Foundation of China (Grant No. 11401310). The second author was supported by National Natural Science Foundation of China (Grant No. 11531005). This work was done while the first author was visiting the Institute of Mathematical Sciences of the Chinese University of Hong Kong. The first author thanks the institution and is very grateful to Professor Zhouping Xin for his invitation.

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Authors and Affiliations

  1. College of Science, Nanjing Forestry University, Nanjing, 210037, China

    Hairong Liu

  2. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Xiaoping Yang

Authors
  1. Hairong Liu
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  2. Xiaoping Yang
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Correspondence to Hairong Liu.

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Liu, H., Yang, X. Strong unique continuation property for a class of fourth order elliptic equations with strongly singular potentials. Sci. China Math. 65, 707–730 (2022). https://doi.org/10.1007/s11425-020-1734-8

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  • DOI: https://doi.org/10.1007/s11425-020-1734-8

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