A survey on boundary conditions for the biharmonic

Abstract

For second-order elliptic equations one usually extensively studies the case of Dirichlet boundary conditions and other boundary conditions are left to the reader. For the biharmonic equation Δ2 u = f on a bounded domain in ℝ n it is not that obvious which boundary condition would serve as a role model. Usually a good approach is to focus on some boundary conditions which describe physically relevant situations. We will discuss boundary conditions for a slender beam and for the thin elastic plate.