2019
Том 71
№ 11

All Issues

Regularity of a Boundary Point for Degenerate Parabolic Equations with Measurable Coefficients

Skrypnik I. I.

Full text (.pdf)


Abstract

We investigate the continuity of solutions of quasilinear parabolic equations in the neighborhood of the nonsmooth boundary of a cylindrical domain. As a special case, one can consider the equation \(\frac{{\partial u}}{{\partial t}} - \Delta _p u = 0\) with the p-Laplace operator Δp. We prove a sufficient condition for the regularity of a boundary point in terms of C p-capacity.

English version (Springer): Ukrainian Mathematical Journal 52 (2000), no. 11, pp 1768-1786.

Citation Example: Skrypnik I. I. Regularity of a Boundary Point for Degenerate Parabolic Equations with Measurable Coefficients // Ukr. Mat. Zh. - 2000. - 52, № 11. - pp. 1550-1565.

Full text