Ukrainian Mathematical Bulletin

Volume 2, Issue 2, 2005 pp. 223-238.

Harnack Inequality for a Nonlinear Elliptic Equation with Coefficients from the Kato Class

Authors: Igor' I. Skrypnik
Author institution: Institute of Applied Mathematics and Mechanics of NAS of Ukraine, 74 Rosa Luxemburg Str., 83114, Donetsk, Ukraine

Summary: We prove the Harnack inequality for the nonnegative solutions of an elliptic equation $$ -\Delta_p u + \sum^n_{i=1} h_i(x) \,\Big|\frac{\partial u}{\partial x}\Big|^{p-2}\,\,\frac{\partial u}{\partial x_i} + g(x)\,|u|^{p-2} u = 0, $$ where $h_i(x)$ and $g(x)$ belong to the Kato class.

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