Global estimates of fundamental solutions for higher-order Schr\"odinger equations
Analysis of PDEs
2015-06-09 v3 Mathematical Physics
math.MP
Abstract
In this paper we first establish global pointwise time-space estimates of the fundamental solution for Schr\"odinger equations, where the symbol of the spatial operator is a real non-degenerate elliptic polynomial. Then we use such estimates to establish related Lp-Lq estimates on the Schr\"odinger solution. These estimates extend known results from the literature and are sharp. This result was latetly already generalized to a degenerate case (cf. [9]).
Keywords
Cite
@article{arxiv.1104.5367,
title = {Global estimates of fundamental solutions for higher-order Schr\"odinger equations},
author = {JinMyong Kim and Anton Arnold and Xiaohua Yao},
journal= {arXiv preprint arXiv:1104.5367},
year = {2015}
}