Symmetry in nonlinear PDEs: Some open problems

被引：1

作者：

Pisante, Adriano ^{[1
]}

机构：

[1] Univ Roma La Sapienza, Dept Math, I-00185 Rome, Italy

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2014年 / 15卷 / 02期

关键词：

Phase transition; minimal surfaces; Ginzburg-Landau model; Landau-De Gennes model; harmonic maps; local minimizers; GINZBURG-LANDAU EQUATION; DE-GENNES THEORY; NEMATIC LIQUID-CRYSTALS; SADDLE-SHAPED SOLUTIONS; MINIMAL HYPERSURFACES; RADIAL-HEDGEHOG; PHASE-TRANSITIONS; GRADIENT THEORY; MINIMIZERS; CONJECTURE;

D O I：

10.1007/s11784-014-0181-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we discuss symmetry properties of solutions for simple scalar and vector-valued systems of nonlinear elliptic partial differential equations (PDEs). The systems of interest are of variational nature, they appear, for instance, in some first-order phase transition models in mathematical physics (e.g., phase separation, superconductivity, liquid crystals) and are naturally related to some PDEs in geometry (minimal surfaces and harmonic maps). We review some known results and present few open problems about symmetry of minimizers for all these models.

引用

页码：299 / 320

页数：22

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