Boundedness of the negative part of biharmonic Green's functions under Dirichlet boundary conditions in general domains
Hans-Christoph Grunau, Frédéric Robert · Comptes Rendus Mathématique · 2009
In general, higher order elliptic equations and boundary value problems like the biharmonic equation or the linear clamped plate boundary value problem do not enjoy neither a maximum principle nor a comparison principle or – equivalently – a positivity preserving property. It is shown that, on the other hand, for bounded smooth domains Ω ⊂ R n , the negative part of the corresponding Green's function is “small” when compared with its singular positive part, provided that n ⩾ 3 .