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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].

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)
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