Electron. J. Diff. Equ., Vol. 2014 (2014), No. 137, pp. 1-14.

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

Shanming Ji, Jingxue Yin, Rui Huang

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.

Submitted April 3, 2014. Published June 11, 2014.
Math Subject Classifications: 34K37, 46E35, 47H10.
Key Words: Sobolev space; periodic solution; locally Lipschitz potential; AR-condition; nonsmooth C-condition; the least action principle; mountain pass lemma.

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Shanming Ji
School of Mathematical Sciences
South China Normal University
Guangzhou 510631, China
email: sam@m.scnu.edu.cn
Jingxue Yin
School of Mathematical Sciences
South China Normal University
Guangzhou 510631, China
email: yjx@scnu.edu.cn
Rui Huang
School of Mathematical Sciences
South China Normal University
Guangzhou 510631, China
email: huang@scnu.edu.cn

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