Uniqueness and non-existence theorems for conformally invariant equations

被引：45

作者：

Xu, XW ^{[1
]}

机构：

[1] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2005年 / 222卷 / 01期

关键词：

conformally invariant integral equations; method of moving spheres; Q-curvature;

D O I：

10.1016/j.jfa.2004.07.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By using the equivalent integral form for the Q-curvature equation, we generalize the well-known non-existence results on two-dimensional Gaussian curvature equation to all dimensional Q-curvature equation. Somehow, we introduce a new approach to Q-curvature equation which is higher order and even pseudo-differential equation. As a by-product, we do classify the solutions for Q = 1 solutions on S-n as well as on R-n with necessary growth rate assumption. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：1 / 28

页数：28

共 22 条

[1] SCALAR CURVATURE FUNCTIONS IN A CONFORMAL CLASS OF METRICS AND CONFORMAL TRANSFORMATIONS
BOURGUIGNON, JP
EZIN, JP
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 301 (02) : 723 - 736
[2] ASYMPTOTIC SYMMETRY AND LOCAL BEHAVIOR OF SEMILINEAR ELLIPTIC-EQUATIONS WITH CRITICAL SOBOLEV GROWTH
CAFFARELLI, LA
GIDAS, B
SPRUCK, J
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1989, 42 (03) : 271 - 297
[3] Chang A., 1997, MATH RES LETT, V4, P1
[4] PRESCRIBING GAUSSIAN CURVATURE ON S2
CHANG, SYA
YANG, PC
[J]. ACTA MATHEMATICA, 1987, 159 (3-4) : 215 - 259
[5] Chen W., private communication
[6] CLASSIFICATION OF SOLUTIONS OF SOME NONLINEAR ELLIPTIC-EQUATIONS
CHEN, WX
LI, CM
[J]. DUKE MATHEMATICAL JOURNAL, 1991, 63 (03) : 615 - 622
[7] A NECESSARY AND SUFFICIENT CONDITION FOR THE NIRENBERG PROBLEM
CHEN, WX
LI, CM
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1995, 48 (06) : 657 - 667
[8] CHEN WX, 1995, J DIFFER GEOM, V41, P259
[9] On the asymptotic behavior of solutions of the conformal Gaussian curvature equations in R-2
Cheng, KS
Lin, CS
[J]. MATHEMATISCHE ANNALEN, 1997, 308 (01) : 119 - 139
[10] SYMMETRY AND RELATED PROPERTIES VIA THE MAXIMUM PRINCIPLE
GIDAS, B
NI, WM
NIRENBERG, L
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1979, 68 (03) : 209 - 243

← 1 2 3 →