论文标题
$ p $ - 谐波函数通过内在的平均值属性
$p$-harmonic functions by way of intrinsic mean value properties
论文作者
论文摘要
令$ω\ subset \ mathbb {r}^n $为满足均匀外部锥体条件的有限域。我们建立了与$ω$中某些内在的非线性平均值属性相关的Dirichlet问题连续解决方案的存在和唯一性。此外，我们表明，当正确地进行标准化后，此类功能会收敛到$ω$中的dirichlet问题的$ p $ harmonic解决方案，以[2，\ infty）$中的$ p \。存在的证明是建设性的，方法完全是分析性的，这是一种基本工具，是$ω$中$ p $独立的障碍物功能的构建。
Let $Ω\subset\mathbb{R}^n$ be a bounded domain satisfying the uniform exterior cone condition. We establish existence and uniqueness of continuous solutions of the Dirichlet Problem associated to certain intrinsic nonlinear mean value properties in $Ω$. Furthermore we show that, when properly normalized, such functions converge to the $p$-harmonic solution of the Dirichlet problem in $Ω$, for $p\in[2,\infty)$. The proof of existence is constructive and the methods are entirely analytic, a fundamental tool being the construction of explicit, $p$-independent barrier functions in $Ω$.
