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Research Report MRR99-045
The Second Boundary Value Problem for a Class of Hessian
John Urbas
Abstract:
We prove the existence of globally smooth convex
solutions $u$ of a class of Hessian equations subject to the
boundary condition $Du(\Omega) = \Omega^*$ where $\Omega$ and
$\Omega^*$ are smooth uniformly convex domains in {\bf R}$^n$. The
results generalize some of our previous work on the two
dimensional case and on the Monge-Amp\`ere equation in all
dimensions.
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