A right inverse of differential operator $\Delta+a$ in weighted Hilbert space $L^2(\mathbb{R}^n,e^{-|x|^2})$

Shaoyu Dai; Yang Liu; Yifei Pan

A right inverse of differential operator $\Delta+a$ in weighted Hilbert space $L^2(\mathbb{R}^n,e^{-|x|^2})$

Analysis of PDEs 2019-09-30 v1

Authors: Shaoyu Dai , Yang Liu , Yifei Pan

Abstract

In this note, we prove the existence of weak solutions of a Poisson type equation in the weighted Hilbert space $L^2(\mathbb{R}^n,e^{-|x|^2})$ .

Keywords

differential operator right inverse weighted hilbert space poisson equation weak solution

Cite

@article{arxiv.1909.12477,
  title  = {A right inverse of differential operator $\Delta+a$ in weighted Hilbert space $L^2(\mathbb{R}^n,e^{-|x|^2})$},
  author = {Shaoyu Dai and Yang Liu and Yifei Pan},
  journal= {arXiv preprint arXiv:1909.12477},
  year   = {2019}
}