2019
Том 71
№ 6

# Hölder continuity and the Harnack inequality for the solutions of an elliptic equation containing the $p$ -Laplacian and uniformly degenerating in a part of the domain

Huseynov S. T.

Abstract

We consider quasilinear equations of the $p$-Laplacian type uniformly degenerating in a part of the domain. An analog of the Harnack inequality is proved for nonnegative solutions and the Holder continuity of the solutions is established by using this inequality.

Citation Example: Huseynov S. T. Hölder continuity and the Harnack inequality for the solutions of an elliptic equation containing the $p$ -Laplacian and uniformly degenerating in a part of the domain // Ukr. Mat. Zh. - 2017. - 69, № 12. - pp. 1596-1604.