论文标题
在非平滑域上的方形可集成的表面电势，并应用于$ l^2 $的拉普拉斯方程
Square integrable surface potentials on non-smooth domains and application to the Laplace equation in $L^2$
论文作者
论文摘要
在涉及谐波伯格曼投影的流体动力学中应用的动机，我们旨在将单层和双层电势的理论扩展到$ h^1 _ {\ ell oc} $ juromantity的函数的良好文献记载）上，以将其延伸到本地正方形的集成函数。考虑到通常在多边形网格上定义函数的数值模拟，我们希望该理论涵盖非平滑域的案例（即与Lipschitz连续或多边形边界）。
Motivated by applications in fluid dynamics involving the harmonic Bergman projection we aim at extending the theory of single and double layer potentials (well documented for functions with $H^1_{\ell oc}$ regularity) to locally square integrable functions. Having in mind numerical simulations in which functions are usually defined on a polygonal mesh, we wish this theory to cover the cases of non-smooth domains (i.e.with Lipschitz continuous or polygonal boundaries).
