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Strong Unique Continuation of Sub-elliptic Operator on the Heisenberg Group |
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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 |
Page view: 3217
Net amount: 2457 |
Authors: |
Hairong LIU; Xiaoping YANG; |
Foundation: |
the National Natural Science Foundation of China (Nos. 11071119, 11101132). |
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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(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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