Carleman inequalities and unique continuation for the polyharmonic operators
Analysis of PDEs
2022-08-23 v2 Classical Analysis and ODEs
Abstract
We obtain a complete characterization of Carleman estimates with weight 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.
Cite
@article{arxiv.2205.05338,
title = {Carleman inequalities and unique continuation for the polyharmonic operators},
author = {Eunhee Jeong and Yehyun Kwon and Sanghyuk Lee},
journal= {arXiv preprint arXiv:2205.05338},
year = {2022}
}