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 [7][P. G. Ciarlet, 1974] and Monk in [21][P. Monk, 1987] 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.