Solving the biharmonic Dirichlet problem on domains with corners
Résumé
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] and Monk in [21] 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.