Linear Poisson Equations with Potential on Riemann Surfaces

Jiayu Li; Xiangrong Zhu

Linear Poisson Equations with Potential on Riemann Surfaces

Differential Geometry 2025-11-07 v1 Classical Analysis and ODEs

Authors: Jiayu Li , Xiangrong Zhu

Abstract

We study interior estimates for solutions of the linear Poisson equation: $\triangle u = g u + f$ where $g$ and $f$ belong to the Zygmund space $L\ln L$ on a Riemann surface $M$ satisfying the isoperimetric inequality. As applications, we derive corresponding interior estimates, Harnack inequalities, and a global estimate.

Keywords

gradient estimates partial differential equations

Cite

@article{arxiv.2511.04323,
  title  = {Linear Poisson Equations with Potential on Riemann Surfaces},
  author = {Jiayu Li and Xiangrong Zhu},
  journal= {arXiv preprint arXiv:2511.04323},
  year   = {2025}
}

Comments

15 pages

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