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Positive Liouville theorems and asymptotic behavior for p-Laplacian type elliptic equations with a Fuchsian potential

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Martin Fraas, Yehuda Pinchover

Analysis of PDEs · Submitted 29 Mar 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We study positive Liouville theorems and the asymptotic behavior of positive solutions of p-Laplacian type elliptic equations of the form Q'(u):= - pLaplace(u) + V |u|^{p-2} u = 0 in X, where X is a domain in R^d, d > 1, and 1<p<infty.

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arXiv ID1003.5452 (version 2)
Pith IDRC36KV7T, Pith's permanent record of this paper and its review
CitationMartin Fraas, Yehuda Pinchover. "Positive Liouville theorems and asymptotic behavior for p-Laplacian type elliptic equations with a Fuchsian potential." arXiv:1003.5452 (2010). https://pith.science/paper/RC36KV7T
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,568 input tokens, $0.0001 reported.

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arXiv listing abstract v2. Results and the main claim are underlined; .

We study positive Liouville theorems and the asymptotic behavior of positive solutions of p-Laplacian type elliptic equations of the form Q'(u):= - pLaplace(u) + V |u|^{p-2} u = 0 in X, where X is a domain in R^d, d > 1, and 1<p<infty. We assume that the potential V has a Fuchsian type singularity at a point zeta, where either zeta=infty and X is a truncated C^2-cone, or zeta=0 and zeta is either an isolated point of a boundary of X or belongs to a C^2-portion of the boundary of X.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study positive Liouville theorems and the asymptotic behavior of positive solutions of p-Laplacian type elliptic equations of the form Q'(u):= - pLaplace(u) + V |u|^{p-2} u = 0 in X, where X is a domain in R^d, d > 1, and 1<p<infty. contribution 0.98 0.85 0.09 asserted 0.93
s1 We assume that the potential V has a Fuchsian type singularity at a point zeta, where either zeta=infty and X is a truncated C^2-cone, or zeta=0 and zeta is either an isolated point of a boundary of X or belongs to a C^2-portion of the boundary of X. background 0.41 0.37 0.03 asserted 0.98

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Original abstract

We study positive Liouville theorems and the asymptotic behavior of positive solutions of p-Laplacian type elliptic equations of the form Q'(u):= - pLaplace(u) + V |u|^{p-2} u = 0 in X, where X is a domain in R^d, d > 1, and 1<p<infty. We assume that the potential V has a Fuchsian type singularity at a point zeta, where either zeta=infty and X is a truncated C^2-cone, or zeta=0 and zeta is either an isolated point of a boundary of X or belongs to a C^2-portion of the boundary of X.

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