Relationship between variational problems with norm constraints and ground state of semilinear elliptic equations in R²

Hashizume, Masato

Calculus of Variations and Partial Differential Equations, 2024, 63, 131

Number of Access:200（2026-02-18 04:26 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/96462

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Title
Relationship between variational problems with norm constraints and ground state of semilinear elliptic equations in R²
Creator
NRID
1000020836712 1000020836712
researchmap permalink
mhashizume mhashizume
Scopus Author ID
56734162900 56734162900
CreatorName
Hashizume, Masato
Subject
35B08 Entire solutions to PDEs
35J15 Second-order elliptic equations
35J60 Nonlinear elliptic equations
energy functionals)
Primary: 35B38 Critical points of functionals in context of PDEs (e.g
Secondary: 35A15 Variational methods applied to PDEs
Description
The version of record of this article, first published in Calculus of Variations and Partial Differential Equations, is available online at Publisher’s website: https://doi.org/10.1007/s00526-024-02710-y.
Abstract
In this paper, we investigate variational problems in R² with the Sobolev norm constraints and with the Dirichlet norm constraints. We focus on property of maximizers of the variational problems. Concerning variational problems with the Sobolev norm constraints, we prove that maximizers are ground state solutions of corresponding elliptic equations, while we exhibit an example of a ground state solution which is not a maximizer of corresponding variational problems. On the other hand, we show that maximizers of maximization problems with the Dirichlet norm constraints and ground state solutions of corresponding elliptic equations are the same functions, up to scaling, under suitable setting.
Publisher
Springer Science and Business Media Deutschland GmbH
Source Title
Calculus of Variations and Partial Differential Equations
Volume (Issue)
63
Page
131
Date of Issued
2024-06-01
Language
English
Handle URL
https://hdl.handle.net/11094/96462
PISSN
09442669
eISSN
14320835
Relation.isIdenticalTo
DOI (Publisher Version)
https://doi.org/10.1007/s00526-024-02710-y
Access Rights
open access
CopyRight
This article is licensed under a Creative Commons Attribution 4.0 International License.
oaire:version
Version of Record
Category
学術雑誌論文 Journal Article