The nonlocal mean-field equation on an interval

被引：3

作者：

DelaTorre, Azahara ^{[1
]}

Hyder, Ali ^{[2
]}

Martinazzi, Luca ^{[3
]}

Sire, Yannick ^{[4
]}

机构：

[1] Albert Ludwigs Univ Freiburg, Freiburg, Germany

[2] Univ British Columbia, Vancouver, BC, Canada

[3] Univ Padua, Padua, Italy

[4] Johns Hopkins Univ, Baltimore, MD USA

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2020年 / 22卷 / 05期

基金：

瑞士国家科学基金会;

关键词：

Mean field and Liouville equation; nonlocal equations; existence of solutions; bubbling phenomena; TRUDINGER-TYPE INEQUALITY; BLOW-UP ANALYSIS; STATISTICAL-MECHANICS; ASYMPTOTIC-BEHAVIOR; ELLIPTIC EQUATION; EXISTENCE; DIMENSION;

D O I：

10.1142/S0219199719500287

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the fractional mean-field equation on the interval I = (-1, 1) (-Delta)(1/2) u = rho e(u)/integral(I)e(u) dx, subject to Dirichlet boundary conditions, and prove that existence holds if and only if rho < 2 pi. This requires the study of blowing-up sequences of solutions. We provide a series of tools in particular which can be used (and extended) to higher-order mean field equations of nonlocal type.

引用

页数：19

共 29 条

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Baraket S, 1998, CALC VAR PARTIAL DIF, V6, P1

[2]

Blumenthal R. M., 1961, Transactions of the American Mathematical Society, V99, P540, DOI DOI 10.2307/1993561

[3] UNIFORM ESTIMATES AND BLOW UP BEHAVIOR FOR SOLUTIONS OF -DELTA-U = V(X)EU IN 2 DIMENSIONS [J].