Solving the biharmonic Dirichlet problem on domains with corners

The biharmonic Dirichlet boundary value problem on a bounded domain is the focus of the present paper. By Riesz' representation theorem the existence and uniqueness of a weak solution is quite direct. The problem that we are interested in appears when one is looking for constructive approximations of a solution. Numerical methods using for example finite elements, prefer systems of second equations to fourth order problems. Ciarlet and Raviart in and Monk in consider approaches through second order problems assuming that the domain is smooth. We will discuss what happens when the domain has corners. Moreover, we will suggest a setting, which is in some sense between Ciarlet-Raviart and Monk, that inherits the benefits of both settings and that will give the weak solution through a system type approach.