# Global versions of Gagliardo-Nirenberg-Sobolev inequality and applications to wave and Klein-Gordon equations

@article{Abbrescia2019GlobalVO,
title={Global versions of Gagliardo-Nirenberg-Sobolev inequality and applications to wave and Klein-Gordon equations},
author={L. Abbrescia and W. Wong},
journal={arXiv: Analysis of PDEs},
year={2019}
}
• Published 2019
• Mathematics
• arXiv: Analysis of PDEs
• We prove global, or space-time weighted, versions of the Gagliardo-Nirenberg interpolation inequality, with $L^p$ ($p < \infty$) endpoint, adapted to a hyperboloidal foliation. The corresponding versions with $L^\infty$ endpoint was first introduced by Klainerman and is the basis of the classical vector field method, which is now one of the standard techniques for studying long-time behavior of nonlinear evolution equations. We were motivated in our pursuit by settings where the vector field… CONTINUE READING
1 Citations

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