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The Harnack inequality in \(\mathbb R^2\) for quasilinear elliptic equations - MaRDI portal

The Harnack inequality in \(\mathbb R^2\) for quasilinear elliptic equations (Q1604975)

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scientific article; zbMATH DE number 1765850
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The Harnack inequality in \(\mathbb R^2\) for quasilinear elliptic equations
scientific article; zbMATH DE number 1765850

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    The Harnack inequality in \(\mathbb R^2\) for quasilinear elliptic equations (English)
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    10 July 2002
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    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).
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    maximum principle
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    two-sided differential inequality
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