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Mathematics Research Report CMA-MRR25-94
On The Dirichlet Problem For Hessian Equations
Neil S. Trudinger
Abstract:
We prove the solvability of the classical Dirichlet problem for Hessian
equations
determined by symmetric functions of the eigenvalues of the Hessian matrix
of second derivatives. We extend the previous investigation of Caffarelli,
Nirenberg and Spruck and others, through conditions embracing examples typified
by quotients of elementary symmetric functions. We also provide a new proof of
a crucial second derivative estimate in the cases previously considered,
including
the Monge-Ampère equations.
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