The Classification of all weak solutions to $-\Delta u={u^{-\gamma}}$ in the half-space

Luigi Montoro; Luigi Muglia; Berardino Sciunzi

The Classification of all weak solutions to $-\Delta u={u^{-\gamma}}$ in the half-space

Analysis of PDEs 2025-05-15 v2 Functional Analysis

Authors: Luigi Montoro , Luigi Muglia , Berardino Sciunzi

Abstract

We provide the classification of all the positive solutions to $-\Delta u=\frac{1}{u^\gamma}$ in the half space, under minimal assumption.

Keywords

weak solutions half-space Laplace equation classification positive solutions

Cite

@article{arxiv.2404.03343,
  title  = {The Classification of all weak solutions to $-\Delta u={u^{-\gamma}}$ in the half-space},
  author = {Luigi Montoro and Luigi Muglia and Berardino Sciunzi},
  journal= {arXiv preprint arXiv:2404.03343},
  year   = {2025}
}