On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach

Details On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach

2009-01-26

arxiv.org/abs/0901.3986v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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