Acta mathematica scientia, Series B >
A HARNACK TYPE INEQUALITY FOR SOME CONFORMALLY INVARIANT EQUATIONS ON HALF EUCLIDEAN SPACE
Received date: 2009-04-16
Online published: 2009-07-20
Supported by
The research of Yanyan Li was Partially supported by NSF grant DMS-0701545
We establish a Harnack type inequality on half Euclidean space for general conformally invariant fully nonlinear elliptic equations of second order.
Key words: Harnack; conformally invariant; elliptic
Aobing Li , YanYan Li . A HARNACK TYPE INEQUALITY FOR SOME CONFORMALLY INVARIANT EQUATIONS ON HALF EUCLIDEAN SPACE[J]. Acta mathematica scientia, Series B, 2009 , 29(4) : 1105 -1112 . DOI: 10.1016/S0252-9602(09)60089-8
[1] Caffarelli L, Nirenberg L, Spruck J. The Dirichlet problem for nonlinear second-order elliptic equations,
III: Functions of the eigenvalues of the Hessian. Acta Math, 1985, 155: 261–301
[2] Guan P, Wang G. Local estimates for a class of fully nonlinear equations arising from conformal geometry.
Int Math Res Not, 2003, (26): 1413–1432
[3] Li A, Li Y Y. On some conformally invariant fully nonlinear equations. Comm Pure Appl Math, 2003, 56:
1416–1464
[4] Li A, Li Y Y. Private notes, 2003
[5] Li A, Li Y Y. On some conformally invariant fully nonlinear equations, Part II: Liouville, Harnack and Yamabe. arXiv: math.AP/0403442 v1 25 Mar 2004
[6] Li A, Li Y Y. On some conformally invariant fully nonlinear equations, Part II: Liouville, Harnack and Yamabe. Acta Math, 2005, 195: 117–154
[7] Li A, Li Y Y. A fully nonlinear version of the Yamabe problem on manifolds with boundary. J Eur Math Soc, 2006, 8: 295–316
[8] Li Y Y. Local gradient estimates of solutions to some conformally invariant fully nonlinear equations.
arXiv: math.AP/0605559; to appear in Comm Pure Appl Math
[9] Li Y Y, Zhang L. Liouville type theorems and Harnack type inequalities for semilinear elliptic equations. Journal d′Analyse Mathematique, 2003, 90: 27–87
[10] Schoen R. Courses at Stanford University, 1988, and New York University, 1989
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