RECENT PROGRESS ON STABLE AND FINITE MORSE INDEX SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS

被引：0
作者：
Wang, Kelei [1 ]
机构：
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
来源：
ELECTRONIC RESEARCH ARCHIVE | 2021年 / 29卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Stable solutions; finite Morse index solutions; Liouville theorem; De Giorgi conjecture; ALLEN-CAHN EQUATION; LIOUVILLE-TYPE THEOREMS; LANE-EMDEN EQUATION; R-N; PARTIAL REGULARITY; MINIMAL-SURFACES; MONOTONICITY FORMULA; POSITIVE SOLUTIONS; SINGULAR SOLUTIONS; DIRICHLET PROBLEMS;
D O I：
10.3934/era.2021062
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We discuss some recent results (mostly from the last decade) on stable and finite Morse index solutions of semilinear elliptic equations, where Norman Dancer has made many important contributions. Some open questions in this direction are also discussed.
引用
收藏
页码：3805 / 3816
页数：12
相关论文
共 86 条
  • [1] Higher-Dimensional Catenoid, Liouville Equation, and Allen-Cahn Equation
    Agudelo, Oscar
    del Pino, Manuel
    Wei, Juncheng
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2016, 2016 (23) : 7051 - 7102
  • [2] ALT HW, 1981, J REINE ANGEW MATH, V325, P105
  • [3] ALT HW, 1986, J REINE ANGEW MATH, V368, P63
  • [4] Entire solutions of semilinear elliptic equations in R3 and a conjecture of De Giorgi
    Ambrosio, L
    Cabré, X
    [J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 13 (04) : 725 - 739
  • [5] [Anonymous], 2002, Advances in Partial Di erential Equations
  • [6] Brezis H., 2003, NEW STUD ADV MATH, P23
  • [7] Stable solutions to semilinear elliptic equations are smooth up to dimension 9
    Cabre, Xavier
    Ros-Oton, Xavier
    Figalli, Alessio
    Serra, Joaquim
    [J]. ACTA MATHEMATICA, 2020, 224 (02) : 187 - 252
  • [8] Stable s-minimal cones in R3 are flat for s ∼ 1
    Cabre, Xavier
    Cinti, Eleonora
    Serra, Joaquim
    [J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2020, 764 : 157 - 180
  • [9] Nonlocal Minimal Surfaces
    Caffarelli, L.
    Roquejoffre, J. -M.
    Savin, O.
    [J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2010, 63 (09) : 1111 - 1144
  • [10] Caffarelli LA, 2004, CONTEMP MATH, V353, P43
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