The Harnack inequality in \(\mathbb R^2\) for quasilinear elliptic equations
The authors consider the model quasilinear elliptic differential equation \[ \text{div} \biggl\{A\bigl( |Du|\bigr) Du\biggr\}-f(u)=0,\;u> 0 \tag{1} \] in \(\mathbb{R}^2\) and more generally, the two-sided differential inequality \[ -B(Du)\leq \text{div} \biggl\{A\bigl(|Du|\bigr) Du \biggr\} \leq B(Du)+f(u),\;u>0. \tag{2} \] Here, the authors use a maximum principle to obtain a Harnack inequality for (2).
scientific article; zbMATH DE number 1765850