A uniqueness result for viscosity solutions of second order fully nonlinear partial di
A uniqueness result for viscosity solutions of second order fully nonlinear partial di
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DOI：
10.1090/s0002-9939-1988-0934877-2
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发表时间：
1988-04
期刊：
影响因子：
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通讯作者：
R. Jensen;P. Lions;P. Souganidis
中科院分区：
文献类型：
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作者：
R. Jensen;P. Lions;P. Souganidis
本文推广了R.Jensen关于纯量、二阶、完全非线性、椭圆型、可能退化的偏微分方程粘性解的唯一性的一些最新结果。在这篇注记中，我们考虑了形式为F(d2(X0)，d4>；(X0)，u(X0)，x0)(X0)，u(Xo)，xo)>；0的标量二阶非线性椭圆型偏微分方程粘性解的唯一性问题。函数v是(1)的粘性解，如果它既是上解又是下解。
In this note we extend some recent results of R. Jensen concern- ing the uniqueness of viscosity solutions of scalar, second order, fully nonlinear, elliptic, possibly degenerate, partial differential equations. In this note we consider the problem of uniqueness of viscosity solutions of scalar second order nonlinear elliptic, possibly degenerate, partial differential equations of the form F(D2 (x0), D4>(x0),u(x0), x0) (x0),u(xo),xo) > 0) for all . The function v is a viscosity solution of (1), if it is both sub- and supersolution.