Abstract
Consider the higher order parabolic operator and the higher order Schrödinger operator
in
where m and n are any positive integers. Under certain lower order and regularity assumptions, we prove that if solutions to the linear problems vanish when
then the solutions vanish in X. Such results are global if n > 1, and we also prove some relevant local results.
Acknowledgements
The author was visiting The University of Chicago (from Huazhong University of Science and Technology, supported by the China Scholarship Council), while this research was carried out, and he thanks Carlos E. Kenig for fruitful discussion on this work. The author also thanks Quan Zheng for some helpful discussion on related topics, and the anonymous referee for the advice on the exposition of this manuscript.