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

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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.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 6, pp. 818–836, June, 2004.

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Skrypnik, I.I. A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients. Ukr Math J 56, 973–995 (2004). https://doi.org/10.1007/PL00022188

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  • DOI: https://doi.org/10.1007/PL00022188

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