A Trudinger-Moser inequality for conical metric in the unit ball

2018/08/16 by Yang, Yunyan, Zhu, Xiaobao · 1 citation
#35J15 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.05316

Abstract

In this note, we prove a Trudinger-Moser inequality for conical metric in the unit ball. Precisely, let \mathbbB be the unit ball in ℝ^N (N≥ 2), p>1, g=|x|^(2p)/(N)β(dx₁²+⋯+dx_N²) be a conical metric on \mathbbB, and λ_p(\mathbbB)=inf\∫_\mathbbB|∇ u|^Ndx: u∈ W₀^1,N(\mathbbB), ∫_\mathbbB|u|^pdx=1\. We prove that for any β≥ 0 and α

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