Constraint minimizers of mass critical fractional Kirchhoff equations: concentration and uniqueness

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F25%3APU156196" target="_blank" >RIV/00216305:26220/25:PU156196 - isvavai.cz</a>

Výsledek na webu

<a href="https://iopscience-iop-org.ezproxy.lib.vutbr.cz/article/10.1088/1361-6544/adbc3b/pdf" target="_blank" >https://iopscience-iop-org.ezproxy.lib.vutbr.cz/article/10.1088/1361-6544/adbc3b/pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1361-6544/adbc3b" target="_blank" >10.1088/1361-6544/adbc3b</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Constraint minimizers of mass critical fractional Kirchhoff equations: concentration and uniqueness

Popis výsledku v původním jazyce

This paper focuses on the constraint minimization problem associated with the fractional Kirchhoff equation { ( a + b ∫ ℝ N | ( − Δ ) s 2 u | 2 d x ) ( − Δ ) s u + | x | 2 u = μ u + β u 8 s N + 1 in ℝ N , [ 6 p t ] ∫ ℝ N | u | 2 d x = 1 , where s ∈ ( N / 4 , 1 ) , N = 2 , 3 , a ⩾ 0 , b > 0 are constants, μ ∈ R is the corresponding Lagrange multiplier and ( − Δ ) s is the fractional Laplacian operator, 8 s / N + 1 is the corresponding mass critical exponent. The purpose of this paper is threefold: to establish the existence and non-existence of the L2-constraint minimizers to the degenerate fractional Kirchhoff problem, that is a = 0, to prove some classical concentration behaviors of constraint minimizers and to reveal the local uniqueness of constraint minimizers of above problem under double nonlocal effect. In particular, we will give some energy estimates, decay estimates and uniform regularity to find that the maximal point of constraint minimizer concentrates on the bottom point of the homogeneous potential. Furthermore, we introduce several new techniques based on the combination of the localization method of ( − Δ ) s and by establishing the nonlocal Pohozăev identity, which allow us to get over some new challenges due to the nonlocal property of ( − Δ ) s and the fact that ∫ R N | ( − Δ ) s 2 u | 2 d x ( − Δ ) s u does not vanish as a ↘ 0 . We believe that these techniques will have some potential applications in various related problems.

Název v anglickém jazyce

Constraint minimizers of mass critical fractional Kirchhoff equations: concentration and uniqueness

Popis výsledku anglicky

This paper focuses on the constraint minimization problem associated with the fractional Kirchhoff equation { ( a + b ∫ ℝ N | ( − Δ ) s 2 u | 2 d x ) ( − Δ ) s u + | x | 2 u = μ u + β u 8 s N + 1 in ℝ N , [ 6 p t ] ∫ ℝ N | u | 2 d x = 1 , where s ∈ ( N / 4 , 1 ) , N = 2 , 3 , a ⩾ 0 , b > 0 are constants, μ ∈ R is the corresponding Lagrange multiplier and ( − Δ ) s is the fractional Laplacian operator, 8 s / N + 1 is the corresponding mass critical exponent. The purpose of this paper is threefold: to establish the existence and non-existence of the L2-constraint minimizers to the degenerate fractional Kirchhoff problem, that is a = 0, to prove some classical concentration behaviors of constraint minimizers and to reveal the local uniqueness of constraint minimizers of above problem under double nonlocal effect. In particular, we will give some energy estimates, decay estimates and uniform regularity to find that the maximal point of constraint minimizer concentrates on the bottom point of the homogeneous potential. Furthermore, we introduce several new techniques based on the combination of the localization method of ( − Δ ) s and by establishing the nonlocal Pohozăev identity, which allow us to get over some new challenges due to the nonlocal property of ( − Δ ) s and the fact that ∫ R N | ( − Δ ) s 2 u | 2 d x ( − Δ ) s u does not vanish as a ↘ 0 . We believe that these techniques will have some potential applications in various related problems.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

NONLINEARITY

ISSN

0951-7715

e-ISSN

1361-6544

Svazek periodika

38

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

46

Strana od-do

„“-„“

Kód UT WoS článku

001443870900001

EID výsledku v databázi Scopus

2-s2.0-105000363566