This article is cited in 4 papers

Boundary Properties of Solutions to Second-Order Parabolic Equations in Domains with Special Symmetry

I. T. Mamedov

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences

Abstract: We consider the first boundary-value problem for second-order nondivergent parabolic equations with, in general, discontinuous coefficients. We study the regularity of a boundary point assuming that in a neighborhood of this point the boundary of the domain is a surface of revolution. We prove a necessary and sufficient regularity condition in terms of parabolic capacities; for the heat equation this condition coincides with Wiener"s criterion.

UDC: 517.956.4

Received: 29.09.1999

DOI: 10.4213/mzm751

 English version: Mathematical Notes, 2001, 70:3, 347–362

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