On a nonlinear elliptic equation arising in a free boundary problem

Guofang Wang; Dong Ye

doi:10.1007/s00209-003-0493-3

On a nonlinear elliptic equation arising in a free boundary problem

Guofang Wang^*
, Dong Ye

^*此作品的通讯作者

Max Planck Institute for Mathematics in the Sciences
CY Cergy Paris Université
Ecole Normale Supérieure Paris Saclay

科研成果: 期刊稿件 › 文章 › 同行评审

18 引用（Scopus）

摘要

Let p* = n/(n -2) and n ≥ 3. In this paper, we first classify all non-constant solutions of { -Δu = u₊^p* in ℝⁿ, ∫_ℝnu₊^p*dx < ∞. We then establish a sup + inf and a Moser-Trudinger type inequalities for the equation -Δu = u₊^p* . Our results illustrate that this equation is much closer to the Liouville problem -Δu = e^u in dimension two than the usual critical exponent equation, namely -Δu = u^n+2/n-2 is.

源语言	英语
页（从-至）	531-548
页数	18
期刊	Mathematische Zeitschrift
卷	244
期	3
DOI	https://doi.org/10.1007/s00209-003-0493-3
出版状态	已出版 - 7月 2003
已对外发布	是

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abstract = "Let p* = n/(n -2) and n ≥ 3. In this paper, we first classify all non-constant solutions of \{ -Δu = u+p* in ℝn, ∫ℝnu+p*dx < ∞. We then establish a sup + inf and a Moser-Trudinger type inequalities for the equation -Δu = u+p* . Our results illustrate that this equation is much closer to the Liouville problem -Δu = eu in dimension two than the usual critical exponent equation, namely -Δu = un+2/n-2 is.",

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AB - Let p* = n/(n -2) and n ≥ 3. In this paper, we first classify all non-constant solutions of { -Δu = u+p* in ℝn, ∫ℝnu+p*dx < ∞. We then establish a sup + inf and a Moser-Trudinger type inequalities for the equation -Δu = u+p* . Our results illustrate that this equation is much closer to the Liouville problem -Δu = eu in dimension two than the usual critical exponent equation, namely -Δu = un+2/n-2 is.

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On a nonlinear elliptic equation arising in a free boundary problem

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