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

  • I. I. Skrypnik

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.
Published
25.06.2004
How to Cite
SkrypnikI. I. “A Necessary Condition for the Regularity of a Boundary Point for Degenerating Parabolic Equations With Measurable Coefficients”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 6, June 2004, pp. 818–836, https://umj.imath.kiev.ua/index.php/umj/article/view/3801.
Section
Research articles