TY - JOUR
T1 - The Uniqueness of Viscosity Solutions of the Second Order Fully Nonlinear Elliptic Equations
JO - Journal of Partial Differential Equations
VL - 1
SP - 77
EP - 84
PY - 1988
DA - 1988/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5855.html
KW -
AB - Recently R. Jensen [1] has proved the uniqueness of viscosity solutions in W^{1,∞} of second order fully nonlinear elliptic equation F (D², Du, u) = 0. He does not assume F to be convex. In this paper we extend his result [1] to the case that F can be dependent on x, i. e. prove that the viscosity solutions in W^{1,∞} of the second order fully nonlinear elliptic equation F (D²u, Du, u, x) = 0 are unlique. We do not assume F to be convex either.