Sobolev regularity of the second biharmonic problem on a rectangle

Summary It is proved that for any f &esin; L²(Ω) the weak solution of the second biharmonic problem on a rectangle satisfies u&esin; H⁴(Ω). The proof uses the decomposition of the problem into two Poisson equations and a general condition for H⁴-regularity via the eigenvalues and eigenfunctions of second order elliptic operators.