Classification results for bounded positive solutions to the critical $p$-Laplace equation

Giulio Ciraolo; Michele Gatti

Classification results for bounded positive solutions to the critical $p$-Laplace equation

Analysis of PDEs 2026-01-27 v2

Authors: Giulio Ciraolo , Michele Gatti

Abstract

By providing optimal or nearly optimal integral estimates, we show that every positive, bounded or moderately growing, local weak solution to the critical $p$ -Laplace equation in $\mathbb{R}^n$ , with $n\geq 3$ , and whose infimum over a ball behaves properly must be a bubble.

Keywords

critical p-Laplace equation bounded positive solutions integral estimates bubble weak solutions

Cite

@article{arxiv.2510.23243,
  title  = {Classification results for bounded positive solutions to the critical $p$-Laplace equation},
  author = {Giulio Ciraolo and Michele Gatti},
  journal= {arXiv preprint arXiv:2510.23243},
  year   = {2026}
}

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