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A variational proof of Nash’s inequality

Bouin, Emeric; Dolbeault, Jean; Schmeiser, Christian (2020), A variational proof of Nash’s inequality, Atti della Accademia Nazionale dei Lincei. Classe di scienze fisiche, matematiche e naturali, Matematica e applicazioni, 31, 1, p. 211-223. 10.4171/RLM/886

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Atti della Accademia Nazionale dei Lincei. Classe di scienze fisiche, matematiche e naturali, Matematica e applicazioni
Volume
31
Number
1
Publisher
Springer
Pages
211-223
Publication identifier
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Author(s)
Bouin, Emeric
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dolbeault, Jean cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Schmeiser, Christian
Fakultät für Mathematik [Wien]
Abstract (EN)
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.
Subjects / Keywords
compact support; compactness; semi-linear elliptic equations; Nash inequality; interpolation; radial symmetry; Neumann homogeneous boundary conditions; Laplacian