Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. III. Uniqueness of viscosity solutions for general second-order equations
Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. III. Uniqueness of viscosity solutions for general second-order equations
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DOI：
10.1016/0022-1236(89)90062-1
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发表时间：
1989-09
影响因子：
1.7
通讯作者：
P. Lions
中科院分区：
文献类型：
--
作者：
P. Lions
本文证明了无穷维Hilbert空间中一类完全非线性二阶方程粘性解的存在性和唯一性。唯一性证明使用所谓的inf和超级卷积，允许一些减少有限维问题。
We prove here the uniqueness and existence of viscosity solutions for a general class of fully nonlinear second-order equations in an infinite-dimensional Hilbert space. The uniqueness is proved using the so-called inf and sup convolutions which allow some reduction to finite-dimensional problems.