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arXiv · 2205.05338

Carleman inequalities and unique continuation for the polyharmonic operators

Eunhee Jeong·Yehyun Kwon·Sanghyuk Lee
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Abstract

We obtain a complete characterization of $L^p-L^q$ Carleman estimates with weight $e^{v\cdot x}$ 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 Schr\"odinger equations relaxing the integrability assumption on the solution spaces.

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Eunhee Jeong, Yehyun Kwon, Sanghyuk Lee. 2022-05-11. Carleman inequalities and unique continuation for the polyharmonic operators. https://arxiv.org/abs/2205.05338

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