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Conformally invariant Monge-Ampère equations: Global solutions
Author(s):
Jeff
A.
Viaclovsky
Journal:
Trans. Amer. Math. Soc.
352
(2000),
4371-4379.
MSC (2000):
Primary 35J60, 53A30
Posted:
April 17, 2000
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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  . These equations are elliptic and variational. Using this structure and the conformal invariance, we will prove a global uniqueness theorem for solutions in  with a quadratic growth condition at infinity.
References:
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- Lars Garding, An inequality for hyperbolic polynomials, J. Math. Mech. 8 (1959), 957-965. MR 2:4809
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- J. Viaclovsky, Conformal geometry, contact geometry and the calculus of variations, Duke Math. J. 101 (2000), no. 2, 283-316.
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- Xu Jia Wang, A class of fully nonlinear elliptic equations and related functionals, Indiana Univ. Math. J. 43 (1994), no. 1, 25-54. MR 95f:35089
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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:
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
Posted:
April 17, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
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