In this paper, we establish the global C2,α and W2,p regularity for the Monge-Ampère equation detD2u= f subject to boundary condition Du(Ω)= Ω*, where Ω and Ω* are bounded convex domains in the Euclidean space Rn with C1,1 boundaries, and f is a Hölder continuous function. This boundary value problem arises naturally in optimal transportation and many other application
Abstract. It is well-known that the Dirichlet problem for the Monge-Ampère equation detD2u = µ in a...
We survey old and new regularity theory for the Monge-Ampère equation, show its connection to optima...
We survey old and new regularity theory for the Monge-Ampère equation, show its connection to optima...
Abstract. We develop an ε-regularity theory at the boundary for a general class of Monge-Ampère typ...
This paper is concerned with the existence of globally smooth solutions for the second boundary valu...
In this paper we first introduce a transform for convex functions and use it to prove a Bernstein th...
Boundary C^{2,\alpha} estimates for Monge-Ampere type equations In this paper, we obtain global seco...
Abstract. We study the properties of generalized solutions to the Monge– Ampère equation detD2u = ν...
In this thesis we study the regularity problem in optimal transportation, by establishing the a prio...
On a smooth domain ⊂⊂ Cn,we consider the Dirichlet problem for the complex Monge-Ampère equation ((d...
This paper establishes boundary estimates for solutions to the parabolic Monge-Ampere equation ut (d...
Abstract. It is well-known that the Dirichlet problem for the Monge-Ampère equation detD2u = µ in a...
We consider some recent regularity results for the Monge-Ampère equation arising in the optimal tran...
Abstract. In this note we prove that, if the cost function satisfies some necessary structural con-d...
The global-regularity for the graph of solutions to a singular Monge–Ampère equation was established...
Abstract. It is well-known that the Dirichlet problem for the Monge-Ampère equation detD2u = µ in a...
We survey old and new regularity theory for the Monge-Ampère equation, show its connection to optima...
We survey old and new regularity theory for the Monge-Ampère equation, show its connection to optima...
Abstract. We develop an ε-regularity theory at the boundary for a general class of Monge-Ampère typ...
This paper is concerned with the existence of globally smooth solutions for the second boundary valu...
In this paper we first introduce a transform for convex functions and use it to prove a Bernstein th...
Boundary C^{2,\alpha} estimates for Monge-Ampere type equations In this paper, we obtain global seco...
Abstract. We study the properties of generalized solutions to the Monge– Ampère equation detD2u = ν...
In this thesis we study the regularity problem in optimal transportation, by establishing the a prio...
On a smooth domain ⊂⊂ Cn,we consider the Dirichlet problem for the complex Monge-Ampère equation ((d...
This paper establishes boundary estimates for solutions to the parabolic Monge-Ampere equation ut (d...
Abstract. It is well-known that the Dirichlet problem for the Monge-Ampère equation detD2u = µ in a...
We consider some recent regularity results for the Monge-Ampère equation arising in the optimal tran...
Abstract. In this note we prove that, if the cost function satisfies some necessary structural con-d...
The global-regularity for the graph of solutions to a singular Monge–Ampère equation was established...
Abstract. It is well-known that the Dirichlet problem for the Monge-Ampère equation detD2u = µ in a...
We survey old and new regularity theory for the Monge-Ampère equation, show its connection to optima...
We survey old and new regularity theory for the Monge-Ampère equation, show its connection to optima...
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