InteriorC2,αRegularity for Potential Functions in Optimal Transportation
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Publication:3550968
DOI10.1080/03605300903236609zbMath1189.35142OpenAlexW2066520414MaRDI QIDQ3550968
Jiakun Liu, Xu-Jia Wang, Neil S. Trudinger
Publication date: 8 April 2010
Published in: Communications in Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/03605300903236609
Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Monge-Ampère equations (35J96)
Related Items (34)
Radial solutions for fully nonlinear elliptic equations of Monge-Ampère type ⋮ Stability results on the smoothness of optimal transport maps with general costs ⋮ On the Degeneracy of Optimal Transportation ⋮ On the local theory of prescribed Jacobian equations revisited ⋮ The Monge–Ampère equation and its link to optimal transportation ⋮ A glimpse into the differential topology and geometry of optimal transport ⋮ On the local theory of prescribed Jacobian equations ⋮ Hölder continuity and injectivity of optimal maps ⋮ Strict convexity and \(C^{1,\alpha}\) regularity of potential functions in optimal transportation under condition A3w ⋮ First and second derivative Hölder estimates for generated Jacobian equations ⋮ Strict g-Convexity for Generated Jacobian Equations with Applications to Global Regularity ⋮ Continuity for the Monge mass transfer problem in two dimensions ⋮ Positivity of Ma-Trudinger-Wang curvature on Riemannian surfaces ⋮ Regularity in Monge's mass transfer problem ⋮ A perturbation argument for a Monge-Ampère type equation arising in optimal transportation ⋮ On the local geometry of maps with c-convex potentials ⋮ A note on global regularity in optimal transportion ⋮ Free discontinuities in optimal transport ⋮ Partial \(W^{2,p}\) regularity for optimal transport maps ⋮ Boundary \(\varepsilon\)-regularity in optimal transportation ⋮ On asymptotic behaviour and \(W^{2, p}\) regularity of potentials in optimal transportation ⋮ Continuity and injectivity of optimal maps ⋮ Existence and nonexistence of subsolutions for augmented Hessian equations ⋮ Regularity of optimal transport maps on locally nearly spherical manifolds ⋮ REGULARITY OF MONGE–AMPÈRE EQUATIONS IN OPTIMAL TRANSPORTATION ⋮ Hölder regularity of optimal mappings in optimal transportation ⋮ Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds ⋮ On the Dirichlet problem for degenerate Monge-Ampère type equations ⋮ Necessary and sufficient conditions of entire subsolutions to Monge-Ampère type equations ⋮ Boundary $C^{1,\alpha}$ regularity of an optimal transport problem with cost close to $-x\cdot y$ ⋮ Pointwise Estimates and Regularity in Geometric Optics and Other Generated Jacobian Equations ⋮ Boundary \(C^{2, \alpha}\) estimates for Monge-Ampère type equations ⋮ Partial regularity for optimal transport maps ⋮ Towards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular)
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