Strong Unique Continuation of Sub-elliptic Operator on the Heisenberg Group

Citation:

Hairong LIU,Xiaoping YANG.Strong Unique Continuation of Sub-elliptic Operator on the Heisenberg Group[J].Chinese Annals of Mathematics B,2013,34(3):461~478
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Authors:

Hairong LIU; Xiaoping YANG;

Foundation:

the National Natural Science Foundation of China (Nos. 11071119, 11101132).
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(z,t)u=-X_i(a_{ij}(z,t)X_ju)+V(z,t)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

Classification:

35A02, 35H10, 35R03
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