Stationary Layered Solutions for a System of Allen-Cahn Type Equations

被引：15

作者：

Alessio, Francesca ^{[1
]}

机构：

[1] Univ Politecn Marche, Dipartimento Ingn Ind & Sci Matemat, I-60131 Ancona, Italy

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2013年 / 62卷 / 05期

关键词：

Elliptic systems; variational methods; Brake orbits; CONJECTURE; GIORGI; R-2; SYMMETRY; ORBITS;

D O I：

10.1512/iumj.2013.62.5108

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a class of a semilinear elliptic system of the form (0.1) -Delta u(x, y) + del W(u(x, y)) = 0, (x, y) is an element of R-2 where W : R-2 -> R is a double well nonnegative symmetric potential. We show, via variational methods, that if the set of solutions to the one-dimensional system -q(x) + del W(q(x)) 0, x is an element of R, which connect the two minima of W as x -> +/-infinity, has a discrete structure, then (0.1) has infinitely many layered solutions.

引用

页码：1535 / 1564

页数：30

共 32 条

[1]

Alama S, 1997, CALC VAR PARTIAL DIF, V5, P359, DOI 10.1007/s005260050071

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

Alberti, G ;

Ambrosio, L ;

Cabré, X .

ACTA APPLICANDAE MATHEMATICAE, 2001, 65 (1-3) :9-33

[3]

Alessio F, 2000, CALC VAR PARTIAL DIF, V11, P177, DOI 10.1007/s005260000036

[4] Entire solutions in R2 for a class of Allen-Cahn equations [J].

Alessio, F ;

Montecchiari, P .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2005, 11 (04) :633-672

[5]

Alessio F, 2005, ADV NONLINEAR STUD, V5, P515

[6] Brake orbits type solutions to some class of semilinear elliptic equations [J].

Alessio, Francesca ;

Montecchiari, Piero .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2007, 30 (01) :51-83

[7] On the connection problem for potentials with several global minima [J].

Alikakos, N. D. ;

Fusco, G. .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (04) :1871-1906

[8]

ALIKAKOS N. D., 2010, ELLIPTIC SYSTEM SYMM

[9] Entire Solutions to Equivariant Elliptic Systems with Variational Structure [J].

Alikakos, Nicholas D. ;

Fusco, Giorgio .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 202 (02) :567-597

[10] Entire solutions of semilinear elliptic equations in R3 and a conjecture of De Giorgi [J].

Ambrosio, L ;

Cabré, X .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 13 (04) :725-739

← 1 2 3 4 →