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A variational proof of Nash’s inequality

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Date
2020
Dewey
Analyse
Sujet
compact support; compactness; semi-linear elliptic equations; Nash inequality; interpolation; radial symmetry; Neumann homogeneous boundary conditions; Laplacian
Journal issue
Atti della Accademia Nazionale dei Lincei. Classe di scienze fisiche, matematiche e naturali, Matematica e applicazioni
Volume
31
Number
1
Publication date
03-2020
Article pages
211-223
Publisher
Springer
DOI
http://dx.doi.org/10.4171/RLM/886
URI
https://basepub.dauphine.fr/handle/123456789/20629
Collections
  • CEREMADE : Publications
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Author
Bouin, Emeric
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Dolbeault, Jean
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Schmeiser, Christian
13321 Fakultät für Mathematik [Wien]
Type
Article accepté pour publication ou publié
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.

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