Local and global minimizers for a variational energy involving a fractional norm

被引：117

作者：

Palatucci, Giampiero ^{[1
,2
]}

Savin, Ovidiu ^{[3
]}

Valdinoci, Enrico ^{[4
]}

机构：

[1] Univ Parma, Dipartimento Matemat, I-43124 Parma, Italy

[2] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[3] Columbia Univ, Dept Math, New York, NY 10027 USA

[4] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2013年 / 192卷 / 04期

基金：

美国国家科学基金会;

关键词：

Phase transitions; Nonlocal energy; Gagliardo norm; Fractional Laplacian; CONJECTURE; EQUATIONS; SYMMETRY;

D O I：

10.1007/s10231-011-0243-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study existence, uniqueness, and other geometric properties of the minimizers of the energy functional where denotes the total contribution from Omega in the H (s) norm of u and W is a double-well potential. We also deal with the solutions of the related fractional elliptic Allen-Cahn equation on the entire space . The results collected here will also be useful for forthcoming papers, where the second and the third author will study the I"-convergence and the density estimates for level sets of minimizers.

引用

页码：673 / 718

页数：46

共 28 条

[1] On a long-standing conjecture of E.!De Giorgi:: Symmetry in 3D for general nonlinearities and a local minimality property [J].