In this paper we prove, by a new method, the Harnack inequality for positive solutions of quasilinear elliptic equations in the generalized Orlicz-Sobolev space setting. Our approach is based on the usage of the Φ-functions associated to generalized Φ-functions and the Moser’s iteration technique. As a consequence, we obtain the Hölder continuity of bounded solutions of such equations.

中文翻译：

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广义Orlicz-Sobolev空间中拟线性椭圆型方程的Harnack不等式。

在本文中，我们通过一种新方法证明了广义Orlicz-Sobolev空间设置中拟线性椭圆型方程正解的Harnack不等式。我们的方法基于与广义Φ函数关联的Φ函数的使用以及Moser的迭代技术。结果，我们获得了这类方程的有界解的Hölder连续性。