Recent developments in elliptic partial differential equations of Monge-Ampere type

By Neil S. Trudinger. 2006

66 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bda6c84b8e860c885a81c2302c08dda77c661ac8

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On the Dirichlet problem for Monge-Ampère type equations (2013, methodology): “In [23], the concept of domain A-convexity is introduced extending that of c-convexity in optimal transportation.”
Oblique boundary value problems for augmented Hessian equations I (2015, background): “11) is related to the Schouten tensor in conformal deformation, see [15, 31].”
On the regularity of solutions of optimal transportation problems (2009, result): “We mention that the results obtained in [22, 29] have been exposed by Trudinger in [27].”
Continuity, curvature, and the general covariance of optimal transportation (2007, methodology): “5) is proportional to the Schouten tensor of a conformally flat metric ds2 = e−4u ∑n i=1(dx i)2, so a similar equation occurs in Viaclovsky’s σn-version of the Yamabe problem [45], [46], which has been studied by the many authors in conformal geometry surveyed in [47] and [40].”
Local gradient estimates of solutions to some conformally invariant fully nonlinear equations (2006, background): “Fully nonlinear equations on Riemannian manifolds involving the Schouten tensor have been studied by Viaclovsky in [35] and [36], by Chang, Gursky and Yang in [4] and [3], and by many others; see for example [5], [22], [31], [37], and the references therein.”
Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds (2014, unknown): “In addition to (1.3)-(1.5), (1.7) and (1.15), assume that (1.16) lim t→∞ f(t1) = +∞ where 1 = (1, . . . , 1) ∈ Rn.”
Hölder Continuity and Injectivity of Optimal Maps (2011, background): “Necessity of Trudinger and Wang’s condition for continuity was shown by Loeper [42], who noted its covariance (as did [35] [49]) and some relations to curvature.”
Continuity and injectivity of optimal maps for non-negatively cross-curved costs (2009, background): “Necessity of Trudinger and Wang’s condition for continuity was shown by Loeper [34], who noted its covariance (as did [28] [41]) and some relations to curvature.”