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

• Date: 2017
• Main Authors: Huseynov, S. T., Гусейнов, С. Т.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2017
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1806
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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.