Regularity, positivity and asymptotic vanishing of solutions of a φ-Laplacian

Abstract

In this note we prove that solutions of a φ-Laplacian operator on the entire space ℝN are locally regular (Hölder continuous), positive and vanish at infinity. Mild restrictions are imposed on the right-hand side of the equation. For example, we assume a Lieberman-like condition but the hypothesis of differentiability is dropped. This is in striking contrast with the classical case.

Keywords

• orlicz-sobolev space
• φ-laplacian
• regularity
• asymptotic vanishing
• primary 35p30
• 35j20
• secondary 46e30