Trudinger, Neil S. Recent developments in elliptic partial differential equations of Monge–Ampère type. (English) Zbl 1130.35058 Sanz-Solé, Marta (ed.) et al., Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22–30, 2006. Volume III: Invited lectures. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-022-7/hbk). 291-301 (2006). Summary: 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.For the entire collection see [Zbl 1095.00006]. Cited in 1 ReviewCited in 34 Documents MSC: 35J60 Nonlinear elliptic equations 35B45 A priori estimates in context of PDEs 35J65 Nonlinear boundary value problems for linear elliptic equations 53A30 Conformal differential geometry (MSC2010) Keywords:Fully nonlinear elliptic partial differential equations; Monge-Ampère type; optimal transportation; conformal deformation PDFBibTeX XMLCite \textit{N. S. Trudinger}, in: Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22--30, 2006. Volume III: Invited lectures. Zürich: European Mathematical Society (EMS). 291--301 (2006; Zbl 1130.35058)