Maximum principles, Liouville-type theorems and symmetry results for a general class of quasilinear anisotropic equations

Abstract

This paper is concerned with a general class of quasilinear anisotropic equations. We first derive some maximum principles for two appropriate P-functions, in the sense of Payne (see the book of Sperb [18]). These maximum principles are then employed to obtain a Liouville-type result and a Serrin–Weinberger-type symmetry result.

Keywords

• maximum principles
• anisotropic equations
• liouville theorems
• symmetry
• wulff shapes
• 35b50
• 35j25
• 35p15
• 70h25