论文标题
公制量度空间中的对称和非对称渐近平均值laplacian
Symmetrized and non-symmetrized Asymptotic Mean Value Laplacian in metric measure spaces
论文作者
论文摘要
渐近平均值laplacian -amv laplacian-通过平均积分的限制，将拉普拉斯运算符从$ \ mathbb {r}^n $扩展到公制测量空间。但是，AMV Laplacian通常不是对称操作员。因此，在本文中，考虑了AMV拉普拉斯式的对称版本，并将重点放在何时对称和非对称AMV运算符上。除了Riemannian和3D接触次接触次 - 黎曼语歧管外，我们还表明它们在包括局部AHLFOR的常规空间（具有消失的度量计量边界）的大量度量度量空间上相同。此外，我们研究了两个操作员通常会有所不同的$ \ mathbb {r}^n $加权域的上下文，并在权重消失的点为这些操作员提供具体公式。
The asymptotic mean value Laplacian - AMV Laplacian - extends the Laplace operator from $\mathbb{R}^n$ to metric measure spaces through limits of averaging integrals. The AMV Laplacian is however not a symmetric operator in general. In this paper therefore a symmetric version of the AMV Laplacian is considered, and focus lies on when the symmetric and non-symmetric AMV operators coincide. Besides Riemannian and 3D contact sub-Riemannian manifolds, we show that they are identical on a large class of metric measure spaces including locally Ahlfors regular spaces with vanishing metric-measure boundary. In addition, we study the context of weighted domains of $\mathbb{R}^n$ where the two operators typically differ, and provide concrete formulae for these operators also at points where the weight vanishes.
