# zbMATH — the first resource for mathematics

On maximum principles and Liouville theorems for quasilinear elliptic equations and systems. (English) Zbl 0543.35031
Let $$\vec u$$ be an $${\mathbb{R}}^ N$$-valued function, which is a solution (weak, bounded) of a system of uniformly strongly elliptic quasilinear differential equations with divergence form, in a domain with Lipschitz continuous boundary in $${\mathbb{R}}^ n$$. A strong maximum principle for $$| \vec u|$$ as well as a maximum principle for the components of $$\vec u$$ are obtained under certain assumptions by simply applying the classical maximum principle for single equation and elementary calculations. In case $$n=2$$, a Liouville theorem for $$| \vec u|$$ under weaker assumptions is observed.
Reviewer: K.Chang
##### MSC:
 35J60 Nonlinear elliptic equations 35B50 Maximum principles in context of PDEs 35B35 Stability in context of PDEs
Full Text: