Classical solutions of singular Monge–Ampère equations in a ball☆
Classical solutions of singular Monge–Ampère equations in a ball☆
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DOI：
10.1016/j.jmaa.2004.11.019
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发表时间：
2005-05
影响因子：
1.3
通讯作者：
J. Goncalves;C. Santos
中科院分区：
文献类型：
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作者：
J. Goncalves;C. Santos
我们关注的是凸的，负的，径向对称的经典解的存在性，唯一性和正则性，其中（D2u）是u， B∧RN， N≠1的Hessian，是具有边界∂B的单位球，ψ: bx（0,∞）→[0,∞)是连续的并且ψ(x,t)=ψ(|x|,t)，其中|x|是x的欧几里德范数。主要的兴趣是在ψ在|x|=1和/或u=0的情况下是奇异的，尽管几个非奇异的情况被主要结果所覆盖。我们的证明存在的方法是利用不动点论证和射击方法。通过适当的估计实现唯一性和规律性。
Our concern is on existence, uniqueness and regularity of convex, negative, radially symmetric classical solutions to where (D2u) is the Hessian of u, B⊂RN, N⩾1, is the unit ball with boundary ∂B, ψ:B×(0,∞)→[0,∞) is continuous and ψ(x,t)=ψ(|x|,t), where |x| is the euclidean norm of x. The main interest is in the case ψ is singular at |x|=1 and/or u=0, although several nonsingular cases are covered by the main result. Our approach to show existence, exploits fixed point arguments and the shooting method. Uniqueness and regularity are achieved through suitable estimates.