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arXiv · 1003.5452

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

Martin Fraas·Yehuda Pinchover
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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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Martin Fraas, Yehuda Pinchover. 2010-03-29. Positive Liouville theorems and asymptotic behavior for p-Laplacian type elliptic equations with a Fuchsian potential. https://arxiv.org/abs/1003.5452

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