2017
Том 69
№ 9

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A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients

Skrypnik I. I.

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Abstract

We prove a necessary condition for the regularity of a point on a cylindrical boundary for solutions of second-order quasilinear parabolic equations of divergent form whose coefficients have a superlinear growth relative to derivatives with respect to space variables. This condition coincides with the sufficient condition proved earlier by the author. Thus, we establish a criterion for the regularity of a boundary point similar to the well-known Wiener criterion for the Laplace equation.

English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 6, pp 973-995.

Citation Example: Skrypnik I. I. A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients // Ukr. Mat. Zh. - 2004. - 56, № 6. - pp. 818–836.

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