  It is shown that, for the bi-harmonic equation, an optimal regularity
criterion of the vertex of typical paraboloids can be expressed in terms of
Osgood-Dini integral conditions of Petrovskii's type for the heat equation
derived in 1934. Some extensions of the first Fourier coefficent method to
other PDEs are discussed. A survey on boundary point regularity for elliptic
and parabolic PDEs is enclosed.
