Abstract
We provide a general framework of inequalities induced by theAubry-Mather theory of Hamilton-Jacobi equations. This frameworkdeals with a sufficient condition on functions $f\inC^1(\mathbb R^n)$ and $g\in C(\mathbb R^n)$ inorder 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 thisframework, we provide proofs of the arithmetic mean-geometric meaninequality, Hölder's inequality and Hilbert's inequality in aunified way.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
