A NEGATIVE RESULT ON REGULARITY ESTIMATES OF FINITE RADIAL MORSE INDEX SOLUTIONS TO ELLIPTIC PROBLEMS

被引：0

作者：

Martinez-baena, J. silverio ^{[1
]}

Villegas, Salvador ^{[1
]}

机构：

[1] Univ Granada, Dept Anal Matemat, Granada 18071, Spain

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2025年 / 24卷 / 03期

关键词：

Stability; elliptic problems; radial solutions; Morse index; regularity estimates;

D O I：

10.3934/cpaa.2024092

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the regularity theory of solutions to elliptic partial differential equations often the concept of stability plays the role of a sufficient condition for smoothness. It is a natural question to ask if this holds true for nonstable but finite Morse index solutions. We provide a negative answer showing the existence of sequences of solutions with radial Morse index equal to 1 for which regularity estimates can not be satisfied.

引用

页码：358 / 364

页数：7

共 8 条

[1] SOLUTIONS OF SUPERLINEAR ELLIPTIC-EQUATIONS AND THEIR MORSE INDEXES
BAHRI, A
LIONS, PL
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1992, 45 (09) : 1205 - 1215
[2] Regularity of radial minimizers and extremal solutions of semilinear elliptic equations
Cabre, Xavier
Capella, Antonio
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 238 (02) : 709 - 733
[3] 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
[4] Exact Morse index computation for nodal radial solutions of Lane-Emden problems
De Marchis, Francesca
Ianni, Isabella
Pacella, Filomena
[J]. MATHEMATISCHE ANNALEN, 2017, 367 (1-2) : 185 - 227
[5] Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations
Figalli, Alessio
Zhang, Yi Ru-Ya
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2024, 77 (01) : 3 - 36
[6] SYMMETRY AND RELATED PROPERTIES VIA THE MAXIMUM PRINCIPLE
GIDAS, B
NI, WM
NIRENBERG, L
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1979, 68 (03) : 209 - 243
[7] The behavior of a function on its critical set
Morse, AP
[J]. ANNALS OF MATHEMATICS, 1939, 40 : 62 - 70
[8] Sharp estimates for semi-stable radial solutions of semilinear elliptic equations
Villegas, Salvador
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 262 (07) : 3394 - 3408

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