Minimization of energy integrals associated with the p-Laplacian in R^N for rearrangements

Abstract

In this article, we establish the existence of minimizers for energy integrals associated with the $p$-Laplacian in $\mathbb{R}^N$ with the admissible set being a rearrangement class of a given function. Some representation formulae of the minimizers are also stated.

Keywords

• Sobolev space
• periodic solution
• locally Lipschitz potential
• AR-condition
• nonsmooth C-condition
• the least action principle
• mountain pass lemma