On the fractional Sch\"odinger equation with variable coefficients
Analysis of PDEs
2024-11-05 v1
Abstract
We study the initial value problem (IVP) associated to the semi-linear fractional Sch\"odinger equation with variable coefficients. We deduce several properties of the anisotropic fractional elliptic operator modelling the dispersion relation and use them to establish the local well-posedness for the corresponding IVP. Also, we obtain unique continuation results concerning the solutions of this problem. These are consequences of uniqueness properties that we prove for the fractional elliptic operator with variable coefficients
Cite
@article{arxiv.2411.01300,
title = {On the fractional Sch\"odinger equation with variable coefficients},
author = {C. E. Kenig and D. Pilod and G. Ponce and L. Vega},
journal= {arXiv preprint arXiv:2411.01300},
year = {2024}
}