2017
Том 69
№ 5

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Regularity of a boundary point for singular parabolic equations with measurable coefficients

Skrypnik I. I.

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Abstract

We investigate the continuity of solutions of quasilinear parabolic equations near the nonsmooth boundary of a cylindrical domain. We prove a sufficient condition for the regularity of a boundary point, which coincides with the Wiener condition for the Laplace p-operator. The model case of the equations considered is the equation \(\frac{{\partial u}}{{\partial t}} - \Delta _p u = 0\) with the Laplace p-operator Δ p for 2n / (n + 1) < p < 2.

English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 4, pp 614-627.

Citation Example: Skrypnik I. I. Regularity of a boundary point for singular parabolic equations with measurable coefficients // Ukr. Mat. Zh. - 2004. - 56, № 4. - pp. 506–516.

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