Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations

被引：235

作者：

Capella, Antonio ^{[2
]}

Davila, Juan ^{[3
,4
]}

Dupaigne, Louis ^{[5
]}

Sire, Yannick ^{[1
]}

机构：

[1] Univ Aix Marseille 3, Paul Cezanne LATP, F-13453 Marseille, France

[2] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico

[3] Univ Chile, Dept Ingn Matemat, Santiago, Chile

[4] Univ Chile, CMM, Santiago, Chile

[5] Univ Picardie Jules Verne, UMR CNRS 6140, LAMFA, Amiens, France

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2011年 / 36卷 / 08期

关键词：

Boundary reactions; Extremal solutions; Fractional operators; ELLIPTIC PROBLEMS; MINIMIZERS; BOUNDARY;

D O I：

10.1080/03605302.2011.562954

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate stable solutions of elliptic equations of the type {(-Delta)(s) u = lambda f(u) in B-1 subset of R-n u = 0 on partial derivative B-1, where n >= 2, s is an element of (0, 1), lambda = 0 and f is any smooth positive superlinear function. The operator (-Delta)(s) stands for the fractional Laplacian, a pseudo- differential operator of order 2s. According to the value of lambda, we study the existence and regularity of weak solutions u.

引用

页码：1353 / 1384

页数：32

共 25 条

[1]

[Anonymous], 1964, HDB MATH FUNCTIONS F

[2]

[Anonymous], 1997, Rev. Mat. Univ. Complut. Madrid

[3]

[Anonymous], 1970, SINGULAR INTEGRALS D

[4]

[Anonymous], 1980, Commun. Partial Differ. Equ

[5]

[Anonymous], 1975, SOBOLEV SPACES PURE

[6]

Brezis H., 1996, ADV DIFFERENTIAL EQU, V1, P73

[7] Layer solutions in a half-space for boundary reactions [J].

Cabré, X ;

Solà-Morales, J .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2005, 58 (12) :1678-1732

[8]

Cabre X., NONLINEAR EQUATIONS

[9]

Cabre X, 2007, PURE APPL MATH Q, V3, P801

[10] Regularity of radial minimizers and extremal solutions of semilinear elliptic equations [J].

Cabre, Xavier ;

Capella, Antonio .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 238 (02) :709-733

← 1 2 3 →