Add to ORKGAbstract. In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Ampère equation, with right hand side bounded away from zero and infinity, is W 2;1loc. This is obtained by showing higher integrability a-priori estimates for D2u, namely D2u 2 L logk L for any k 2 N. 1
Abstract. It is well-known that the Dirichlet problem for the Monge-Ampère equation detD2u = µ in a...
We consider the Monge-Ampere equation det D(2)u = b(x) f (u) > 0 in Omega, subject to the singular b...
Abstract. We obtain boundary Hölder gradient estimates and regularity for solutions to the lineariz...
In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Amp\`ere equation, ...
Abstract. In this note we prove that, if the cost function satisfies some necessary structural con-d...
Abstract. We prove that solutions to the Monge-Ampère inequality detD2u ≥ 1 in Rn are strictly conv...
Abstract. We demonstrate that C2,α estimates for the Monge-Ampère equation depend in a highly nonli...
Abstract. We study the properties of generalized solutions to the Monge– Ampère equation detD2u = ν...
Abstract. Let : Rn! R be a function strictly convex and smooth, and = det D2 is the Monge-Amp `er...
In this note we prove that, if the cost function satisfies some necessary structural conditions and ...
Abstract. It is well-known that the Dirichlet problem for the Monge-Ampère equation detD2u = µ in a...
Abstract. We study interior C1,α regularity of viscosity solutions of the par-abolic Monge-Ampére e...
Abstract. A classical result of Aleksandrov allows one to estimate the size of a convex function u a...
In this paper, we establish the global C2,α and W2,p regularity for the Monge-Ampère equation detD2u...
We consider Monge-Ampére equations with the right hand side function close to a constant and from a ...
Abstract. It is well-known that the Dirichlet problem for the Monge-Ampère equation detD2u = µ in a...
We consider the Monge-Ampere equation det D(2)u = b(x) f (u) > 0 in Omega, subject to the singular b...
Abstract. We obtain boundary Hölder gradient estimates and regularity for solutions to the lineariz...
In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Amp\`ere equation, ...
Abstract. In this note we prove that, if the cost function satisfies some necessary structural con-d...
Abstract. We prove that solutions to the Monge-Ampère inequality detD2u ≥ 1 in Rn are strictly conv...
Abstract. We demonstrate that C2,α estimates for the Monge-Ampère equation depend in a highly nonli...
Abstract. We study the properties of generalized solutions to the Monge– Ampère equation detD2u = ν...
Abstract. Let : Rn! R be a function strictly convex and smooth, and = det D2 is the Monge-Amp `er...
In this note we prove that, if the cost function satisfies some necessary structural conditions and ...
Abstract. It is well-known that the Dirichlet problem for the Monge-Ampère equation detD2u = µ in a...
Abstract. We study interior C1,α regularity of viscosity solutions of the par-abolic Monge-Ampére e...
Abstract. A classical result of Aleksandrov allows one to estimate the size of a convex function u a...
In this paper, we establish the global C2,α and W2,p regularity for the Monge-Ampère equation detD2u...
We consider Monge-Ampére equations with the right hand side function close to a constant and from a ...
Abstract. It is well-known that the Dirichlet problem for the Monge-Ampère equation detD2u = µ in a...
We consider the Monge-Ampere equation det D(2)u = b(x) f (u) > 0 in Omega, subject to the singular b...
Abstract. We obtain boundary Hölder gradient estimates and regularity for solutions to the lineariz...