Recent developments in elliptic partial differential equations of Monge�Ampère type
- Autores: Neil S. Trudinger
- Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé
, Javier Soria de Diego , Juan Luis Varona Malumbres , Joan Verdera , Vol. 3, 2006, ISBN 978-3-03719-022-7, págs. 291-302 - Idioma: inglés
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Resumen
In conjunction with applications to optimal transportation and conformal geometry, there has been considerable research activity in recent years devoted to fully nonlinear, elliptic second order partial differential equations of a particular form, given by functions of the Hessian plus a lower order matrix function. Regularity is determined through the behaviour of this function with respect to the gradient variables. We present a selection of second derivative estimates and indicate briefly their application to optimal transportation and conformal deformation of Riemannian manifolds.
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