On uniqueness and existence of viscosity solutions of fully nonlinear second‐order elliptic PDE's
On uniqueness and existence of viscosity solutions of fully nonlinear second‐order elliptic PDE's
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DOI：
10.1002/cpa.3160420103
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发表时间：
1989
影响因子：
3
通讯作者：
H. Ishii
中科院分区：
文献类型：
--
作者：
H. Ishii
我们证明了完全非线性简并椭圆方程粘度解的几个比较和存在定理。其中之一扩展了詹森最近的一些独特成果。有些建立了二阶 Isaacs 方程解的唯一性，因此包括 P.-L 的 Bellman 方程的唯一性结果。狮子。我们的比较结果甚至适用于不连续解，因此佩伦方法很容易得出连续解的存在性。
We prove several comparison and existence theorems for viscosity solutions of fully nonlinear degenerate elliptic equations. One of them extends some recent uniqueness results by Jensen. Some establish the uniqueness of solutions for second-order Isaacs' equations and hence include the uniqueness results for Bellman equations by P.-L. Lions. Our comparison results apply even for discontinuous solutions and so Perron's method readily yields the existence of continuous solutions.