English

Schr\"odinger type equations with singular coefficients and lower order terms

Analysis of PDEs 2024-02-13 v1

Abstract

In this paper we investigate the well-posedness of the Cauchy problem for a Schr\"odinger operator with singular lower order terms. We allow distributional coefficients and we approach this problem via the regularising methods at the core of the theory of very weak solutions. We prove that a very weak solution exists and it is unique modulo negligible perturbations. Very weak solutions converge to classical solutions when the equation coefficients are regular enough.

Keywords

Cite

@article{arxiv.2402.07826,
  title  = {Schr\"odinger type equations with singular coefficients and lower order terms},
  author = {Alexandre Arias Junior and Alessia Ascanelli and Marco Cappiello and Claudia Garetto},
  journal= {arXiv preprint arXiv:2402.07826},
  year   = {2024}
}

Comments

26 pages

R2 v1 2026-06-28T14:46:17.717Z