Anisotropic p-Laplace Equations on long cylindrical domain

Abstract

The main aim of this article is to study the Poisson type problem for anisotropic \(p\)-Laplace type equation on long cylindrical domains. The rate of convergence is shown to be exponential, thereby improving earlier known results for similar type of operators. The Poincaré inequality for a pseudo \(p\)-Laplace operator on an infinite strip-like domain is also studied and the best constant, like in many other situations in literature for other operators, is shown to be the same with the best Poincaré constant of an analogous problem set on a lower dimension.

Keywords

• pseudo \(p\)-laplace equation
• cylindrical domains
• asymptotic analysis