Nonlinear elliptic equations on the upper half space

2019/06/10 by Tang, Sufanf, Wang, Lei, Zhu, Meijun · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.03739

Abstract

In this paper we shall classify all positive solutions of Δu =a u^p on the upper half space H =ℝ₊ⁿ with nonlinear boundary condition ∂ u/∂ t= - b u^q on ∂ H for both positive parameters a, b>0. We will prove that for p ≥ (n+2)/(n-2), 1≤ q

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• The fully nonlinear Loewner-Nirenberg problem: Liouville theorems and counterexamples to local boundary estimates

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