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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Conformally invariant Monge-Ampère equations: Global solutions


Author: Jeff A. Viaclovsky
Journal: Trans. Amer. Math. Soc. 352 (2000), 4371-4379
MSC (2000): Primary 35J60, 53A30
Published electronically: April 17, 2000
MathSciNet review: 1694380
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Abstract:

In this paper we will examine a class of fully nonlinear partial differential equations which are invariant under the conformal group $SO(n+1,1)$. These equations are elliptic and variational. Using this structure and the conformal invariance, we will prove a global uniqueness theorem for solutions in $\mathbf{R}^n$ with a quadratic growth condition at infinity.


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Additional Information

Jeff A. Viaclovsky
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Address at time of publication: Department of Mathematics, University of Texas, Austin, Texas 78712
Email: jeffv@alumni.princeton.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02548-4
PII: S 0002-9947(00)02548-4
Keywords: Monge-Ampère equations, conformally invariant, global solutions
Received by editor(s): November 19, 1998
Published electronically: April 17, 2000
Article copyright: © Copyright 2000 American Mathematical Society