论文标题
在二阶和四阶椭圆系统上，由散装和表面PDE组成：适当性，规律性理论和特征值问题
On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems
论文作者
论文摘要
在本文中，我们研究了二阶和四阶椭圆问题，这些问题不仅包括散装中的泊松方程，而且还包括域边界上的不均匀的laplace-beltrami方程。散装和表面PDE与Dirichlet或Robin类型的边界条件结合。我们指出，Dirichlet和Robin类型边界条件都可以通过我们的形式主义同时处理，而无需更改框架。此外，我们研究了与这些二阶和四阶椭圆系统相关的特征值问题。我们进一步讨论了这些椭圆问题与某些抛物线问题，尤其是艾伦方程和具有动态边界条件的cahn--hilliard方程之间的关系。
In this paper, we study second-order and fourth-order elliptic problems which include not only a Poisson equation in the bulk but also an inhomogeneous Laplace--Beltrami equation on the boundary of the domain. The bulk and the surface PDE are coupled by a boundary condition that is either of Dirichlet or Robin type. We point out that both the Dirichlet and the Robin type boundary condition can be handled simultaneously through our formalism without having to change the framework. Moreover, we investigate the eigenvalue problems associated with these second-order and fourth-order elliptic systems. We further discuss the relation between these elliptic problems and certain parabolic problems, especially the Allen--Cahn equation and the Cahn--Hilliard equation with dynamic boundary conditions.
