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

2009/01/26 by Victor A. Galaktionov, Galaktionov, V. A. · 1 citation
Computer Science · Mathematics · #35K55 #35K65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.0901.3986

openalex publication_date 2009/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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• Existence of variational solutions to doubly nonlinear systems in general noncylindrical domains

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