Author

Yi-Ru-Ya Zhang

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Preprint Sep 2026

A sharp stability inequality of Liouville's theorem for quasiregular mappings on bounded domains

Let $n \ge 3$ and fix $p>n$. We establish a sharp quantitative stability result in $W^{1,p}$ for Liouville's theorem for nonconstant, sense-preserving quasiregular mappings whose outer distortion $K$ is sufficiently close to one. We first reorganize Reshetnyak's classical local argument \cite{R1976}, drawing systematic...

Yi-Ru-Ya Zhang · 0 citations

Preprint Aug 2026

Critical $p$-Laplace equations with monotone coefficients: Liouville classification and a Schoen-type Harnack inequality

We investigate positive weak solutions of the critical $p$-Laplace equation $$ -\Delta_p u = u^{p^*-1} h(u), \qquad 1<p<n, $$ where $h$ is a positive, bounded, continuous, and nonincreasing function. Our first main result is a complete classification of normalized, bounded, positive entire solutions for every equation...

Yi-Ru-Ya Zhang · 3 citations · ⚡2