Comparing variational methods for the hinged Kirchhoff plate with corners

The hinged Kirchhoff plate model contains a fourth order elliptic differential equation complemented with a zeroeth and a second order boundary condition. On domains with boundaries having corners the strong setting is not well‐defined. We here allow boundaries consisting of piecewise C^{2, 1}‐curves connecting at corners. For such domains different variational settings will be discussed and compared. As was observed in the so‐called Saponzhyan–Babushka paradox, domains with reentrant corners need special care. In that case, a variational setting that corresponds to a second order system needs an augmented solution space in order to find a solution in the appropriate Sobolev‐type space.