论文标题
在关键的$ p $ -laplace方程
On the critical $p$-Laplace equation
论文作者
论文摘要
在本文中，我们将$ \ mathbb {r}^n $上关键$ p-$ laplace方程的积极解决方案分类为$ 1 <p <n $，可能具有无限的能量。如果$ n = 2 $，或者$ n = 3 $和$ \ frac 32 <p <2 $，我们证明刚性没有任何其他假设。在剩下的情况下，我们在能量生长条件下或适当控制无穷大的解决方案的分类。我们的假设比文献中已经出现的假设要弱得多。我们还讨论了结果的扩展到Riemannian设置。
In this paper we provide the classification of positive solutions to the critical $p-$Laplace equation on $\mathbb{R}^n$, for $1<p<n$, possibly having infinite energy. If $n=2$, or if $n=3$ and $\frac 32<p<2$ we prove rigidity without any further assumptions. In the remaining cases we obtain the classification under energy growth conditions or suitable control of the solutions at infinity. Our assumptions are much weaker than those already appearing in the literature. We also discuss the extension of the results to the Riemannian setting.
