Regularity for Monge-ampère Equation near the Boundary
نویسنده
چکیده
In this paper we consider the Monge-Ampère equation det(D2u) = f(x) in a convex domain Ω ⊂ IRn subject to the Dirichlet boundary condition u = φ on ∂Ω. We prove that if ∂Ω and φ are C3 smooth, then the solution u ∈ C2+α(Ω). We also give examples to show that if ∂Ω or φ is only C2,1 smooth, the solution may fail to be C2 smooth near the boundary.
منابع مشابه
Regularity and Boundary Behavior of Solutions to Complex Monge–ampère Equations
1. Background 5 2. Plurisubharmonic functions 8 3. The complex Monge–Ampère operator 10 3.1. Bedford’s and Taylor’s definition of the complex Monge–Ampère operator 11 3.2. Cegrell’s definition of the complex Monge–Ampère operator 12 4. The Dirichlet problem for the complex Monge–Ampère operator 14 4.1. Boundary blow-up problems for the complex Monge–Ampère operator 17 4.2. Comparison principles...
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