Recent developments in elliptic partial differential equations of Monge–Ampère type
Neil S. TrudingerAustralian National University, Canberra, Australia
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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.