JournalsrlmVol. 31, No. 1pp. 211–223

A variational proof of Nash’s inequality

  • Emeric Bouin

    Université de Paris Dauphine, France
  • Jean Dolbeault

    Université de Paris Dauphine, France
  • Christian Schmeiser

    Universität Wien, Austria
A variational proof of Nash’s inequality cover
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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.

Cite this article

Emeric Bouin, Jean Dolbeault, Christian Schmeiser, A variational proof of Nash’s inequality. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 1, pp. 211–223

DOI 10.4171/RLM/886