Volume 1, Issue 1
The Uniqueness of Viscosity Solutions of the Second Order Fully Nonlinear Elliptic Equations

Bian Baojun

J. Part. Diff. Eq.,1(1988),pp.77-84

Published online: 1988-01

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  • Abstract

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.

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@Article{JPDE-1-77, author = {}, title = {The Uniqueness of Viscosity Solutions of the Second Order Fully Nonlinear Elliptic Equations}, journal = {Journal of Partial Differential Equations}, year = {1988}, volume = {1}, number = {1}, pages = {77--84}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5855.html} }
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.
Bian Baojun. (1970). The Uniqueness of Viscosity Solutions of the Second Order Fully Nonlinear Elliptic Equations. Journal of Partial Differential Equations. 1 (1). 77-84. doi:
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