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Research Report MRR96-066
Hessian measures
Neil S. Trudinger and Xu-Jia Wang
Abstract:
The Hessian partial differential operators, determined by the elementary
symmetric functions, are extended as weakly continuous mappings from
corresponding cones of continuous functions to Borel measures. The
corresponding Dirichlet problem is shown to be uniquely solvable under
appropriate conditions, thereby extending previous results for integrable
inhomogeneous terms as well as the theory of generalized solutions of
Monge-Ampère equations. We also consider extensions as signed
measures on larger classes of functions and the application to Hessian
integrals.
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