Existence and Regularity of the Reflector Surfaces in $${\mathbb{R}^{n+1}}$$ R n + 1

Polar factorization and monotone rearrangement of vector‐valued functions

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Natural Sciences, Mathematics, Optimization +8

The dirichlet problem for nonlinear second‐order elliptic equations I. Monge‐ampégre equation

Luis Caffarelli, Louis Nirenberg, Joel Spruck · Communications on Pure and Applied Mathematics · 1984 · 797 citations

Natural Sciences, Mathematics, Physics +9

Regularity of Potential Functions of the Optimal Transportation Problem

Xi‐Nan Ma, Neil S. Trudinger, Xu‐Jia Wang · Archive for Rational Mechanics and Analysis · 2005 · 390 citations

Natural Sciences, Mathematics, Optimization +13

The regularity of mappings with a convex potential

Luis Caffarelli · Journal of the American Mathematical Society · 1992 · 381 citations

Natural Sciences, Mathematics, Optimization +7

On the regularity of the monge‐ampère equation det (∂² u/∂x_i ∂x_j) = f(x, u)

Shiu‐Yuen Cheng, Shing–Tung Yau · Communications on Pure and Applied Mathematics · 1977 · 265 citations

Natural Sciences, Mathematics, Differential Equations +8