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arXiv · 1811.12770

A variational proof of Nash's inequality

Emeric Bouin·Jean Dolbeault·Christian Schmeiser
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Abstract

This paper is intended to give a characterization of the optimality case in Nash's inequality, based on methods of nonlinear analysis for elliptic equations and techniques of the calculus of variations. By embedding the problem into a family of Gagliardo-Nirenberg inequalities, this approach reveals why optimal functions have compact support and also why optimal constants are determined by a simple spectral problem.

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Emeric Bouin, Jean Dolbeault, Christian Schmeiser. 2018-11-30. A variational proof of Nash's inequality. https://arxiv.org/abs/1811.12770

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