Electron. J. Differential Equations, Vol. 2017 (2017), No. 79, pp. 1-13.

Harnack's inequality for p-Laplacian equations with Muckenhoupt weight degenerating in part of the domain

Yuriy A. Alkhutov, Sarvan T. Huseynov

In this article we consider quasi-linear second-order elliptic equations of divergence structure with Makenhaupt weight that degenerates over a small part of the domain. We show that the classical Harnack's inequality does not hold in this case, and prove an appropriate Harnack's inequality for the considered equation.

Submitted February 5, 2017. Published March 21, 2017.
Math Subject Classifications: 35j92, 35j65, 35j70, 35j62.
Key Words: p-Laplasian; Muckenhoupt weight; Harnack's inequality

Show me the PDF file (247 KB), TEX file for this article.

Yuriy A. Alkhutov
Stoletov Vladimir State University
Vladimir, Russia
email: yuriy-alkhutov@yandex.ru
Sarvan T. Huseynov
Baku State University
Baku, Azerbaijan
email: sarvanhuseynov@rambler.ru

Return to the EJDE web page