论文标题
在有界亚分析歧管上的拉普拉斯方程式上
On the Laplace equation on bounded subanalytic manifolds
论文作者
论文摘要
我们证明了零件在$ \ mathbb {r}^n $的亚分析界面子曼属上集成的痕迹公式，可能是非关闭的。我们还建立了$ \ MathBf {W}^{1，P} _ \ nabla（m）$，$ m $界面的亚分析歧管的密度结果，这是$ l^p $切线矢量字段$ v $ $ m $上的$ \ nabla v $ l^p $ $ l^p $，$ l^p $，$ l^p $，$ \ nabla $ \ nabla是the nabla nabla nabla nabla nabla nabla nabla is the divive。我们从这些结果中得出了一些存在的定理和带有dirichlet和neumann边界类型条件的拉普拉斯方程解的独特性。然后，我们研究$ p $ -laplace方程，以$ p \ in [1，\ infty）$大。
We prove a trace formula for integration by parts on subanalytic bounded submanifolds of $\mathbb{R}^n$, possibly non closed. We also establish density results for $\mathbf{W}^{1,p}_\nabla (M)$, $M$ bounded subanalytic manifold, which is the space of the $L^p$ tangent vector fields $v$ on $M$ for which $\nabla v$ is $L^p$, where $\nabla$ is the divergence operator. We derive from these results some theorems of existence and uniqueness of solutions of the Laplace equation with Dirichlet and Neumann boundary type conditions. We then study the $p$-Laplace equation, for $p\in [1,\infty)$ large.
