Anisotropic Picone identities and anisotropic Hardy inequalities

Abstract

Abstract In this paper, we derive an anisotropic Picone identity for the anisotropic Laplacian, which contains some known Picone identities. As applications, a Sturmian comparison principle to the anisotropic elliptic equation and an anisotropic Hardy type inequality are shown.

Keywords

• anisotropic Picone identity
• anisotropic Hardy type inequality
• anisotropic elliptic equation
• Sturmian comparison principle