论文标题
在泊松方程的表面上的泊松方程式上有边界状态
On the Poisson Equation on a Surface with a boundary condition in co-normal direction
论文作者
论文摘要
本文认为，在沿着共同正常方向的边界条件的表面上，泊松方程的弱解决方案存在。当外部力属于$ L_0^p $ -Space时，我们应用Lax-Milgram定理和$ h^1 $ functions的某些属性，以表明表面泊松方程的独特弱解决方案，其中$ h^1 $ - 和$ h^1 $ - 和$ l_0^p $ - 功能是其在表面平均值的集成值的值。此外，我们证明弱解决方案是系统的强大$ l^p $解决方案。作为一个应用程序，我们研究$ {\ rm {div}_γ} v = f $的溶解度。构建强大的$ l^p $ suoldut to sufferent泊松方程的主要思想，其边界条件沿共同正常方向构建，以利用dirichlet边界条件的表面泊松方程的解决方案。
This paper considers the existence of weak and strong solutions to the Poisson equation on a surface with a boundary condition in co-normal direction. We apply the Lax-Milgram theorem and some properties of $H^1$-functions to show the existence of a unique weak solution to the surface Poisson equation when the exterior force belongs to $L_0^p$-space, where $H^1$- and $L_0^p$- functions are the ones whose value of the integral over the surface equal to zero. Moreover, we prove that the weak solution is a strong $L^p$-solution to the system. As an application, we study the solvability of ${\rm{div}_Γ} V = F$. The key idea of constructing a strong $L^p$-solution to the surface Poisson equation with a boundary condition in co-normal direction is to make use of solutions to the surface Poisson equation with a Dirichlet boundary condition.
