Inequalities and the Aubry-Mather theory of Hamilton-Jacobi equations

Yasuhiro Fujita; Katsushi Ohmori

doi:10.3934/cpaa.2009.8.683

Article Contents

2009, Volume 8, Issue 2: 683-688. Doi: 10.3934/cpaa.2009.8.683

This issue Previous Article Singular solutions of the Brezis-Nirenberg problem in a ball Next Article On the asymptotic behavior of the Caginalp system with dynamic boundary conditions

Inequalities and the Aubry-Mather theory of Hamilton-Jacobi equations

Yasuhiro Fujita^1, and
Katsushi Ohmori^2,

1.
Department of Mathematics, Faculty of Science, University of Toyama, Toyama 930-8555
2.
Department of Mathematics, Faculty of Human Development, University of Toyama, Toyama 930-8555

Received: February 29, 2008

Revised: June 30, 2008

Published: February 2009

Abstract Related Papers Cited by

Abstract

We provide a general framework of inequalities induced by the Aubry-Mather theory of Hamilton-Jacobi equations. This framework deals with a sufficient condition on functions $f\in C^1(\mathbb R^n)$ and $g\in C(\mathbb R^n)$ in order that $f-g$ takes its minimum over $\mathbb R^n$ on the set {$x\in \mathbb R^n |Df(x)=0$}. As an application of this framework, we provide proofs of the arithmetic mean-geometric mean inequality, Hölder's inequality and Hilbert's inequality in a unified way.

Keywords:

Mathematics Subject Classification: Primary: 49L25; Secondary: 26D15.

Citation:

Article Metrics

HTML views() PDF downloads(92) Cited by(0)

Inequalities and the Aubry-Mather theory of Hamilton-Jacobi equations

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Inequalities and the Aubry-Mather theory of Hamilton-Jacobi equations

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content