Carleman inequalities and unique continuation for the polyharmonic operators

Eunhee Jeong,Yehyun Kwon,Sanghyuk Lee

doi:10.1016/j.jde.2023.12.004

Carleman inequalities and unique continuation for the polyharmonic operators

Eunhee Jeong, Yehyun Kwon + Show 1 more

https://doi.org/10.1016/j.jde.2023.12.004

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Journal: Journal of Differential Equations

Publication Date: Dec 15, 2023

Affiliation: Jeonju National University of Education, Jeonbuk National University, Changwon National University, Seoul National University

#Carleman Inequalities #Unique Continuation + Show 8 more

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Abstract

We obtain a complete characterization of Lp−Lq Carleman estimates with weight ev⋅x for the polyharmonic operators. Our result extends the Carleman inequalities for the Laplacian due to Kenig–Ruiz–Sogge. Consequently, we obtain new unique continuation properties of higher order Schrödinger equations relaxing the integrability assumption on the solution spaces.

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