| On C~(1 ,α) Regularity for Monge- Ampre Equation |
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| 引用本文： | 胡云姣,保继光.On C~(1 ,α) Regularity for Monge- Ampre Equation[J].东北数学,2000(1). |
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| 作者姓名： | 胡云姣 保继光 |
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| 作者单位： | HU Yun jiao (Computer Institute，Beijing Polytechnic University，Beijing，100044) BAO Ji guang (Department of Mathematics，Beijing Normal University，Beijing，100875) |
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| 基金项目： | The abdus salam International Centre for Theoretical Physics and the NNSF!( 1 9771 0 0 9) of China |
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| 摘 要： | In this paper,we consider the well known problem concerning global regularity ofsolutions of the Dirichlet problems for the Monge-Ampère equations. Theorem1 LetΩ be a uniformly convex domain in Rn with the boundary Ω∈ C3,1 ,φ∈ C2 ,1 ( Ω ) and letf be a nonnegative function in Rnsuch thatf1 / n∈ C1 ,1 (Rn) . Then thereexistsa unique convex solution u∈C1 ,1 / 4 (Ω)∩C1 ,1 (Ω) of the Dirichletproblemdet D2 u =f(x) , inΩ (1 )u =φ(x) , on Ω , (2 )where D2 u=Diju] …
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| 关 键 词： | Global C 1 1/4 regularity Monge Ampère equation degenerate and nondegenerate cases |
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