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Strong unique continuation of sub-elliptic operator on the Heisenberg group

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Abstract

In this paper, the Almgren’s frequency function of the following sub-elliptic equation with singular potential on the Heisenberg group:

$$- \mathcal{L}u + V\left( {z,t} \right)u = - X_i \left( {a_{ij} \left( {z,t} \right)X_j u} \right) + V\left( {z,t} \right)u = 0$$

is introduced. The monotonicity property of the frequency is established and a doubling condition is obtained. Consequently, a quantitative proof of the strong unique continuation property for such equation is given.

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Authors and Affiliations

  1. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    Hairong Liu & Xiaoping Yang

  2. School of Science, Nanjing Forestry University, Nanjing, 210037, China

    Hairong Liu

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 of sub-elliptic operator on the Heisenberg group. Chin. Ann. Math. Ser. B 34, 461–478 (2013). https://doi.org/10.1007/s11401-013-0768-x

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  • DOI: https://doi.org/10.1007/s11401-013-0768-x

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