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

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.

Keywords

Heisenberg group / Frequency function / Doubling condition / Strong unique continuation principle

References

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