The Uniqueness of Viscosity Solutions of the Second Order Fully Nonlinear Elliptic Equations

The Uniqueness of Viscosity Solutions of the Second Order Fully Nonlinear Elliptic Equations

Year:    1988

Journal of Partial Differential Equations, Vol. 1 (1988), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1988-JPDE-5855

Journal of Partial Differential Equations, Vol. 1 (1988), Iss. 1 : pp. 77–84

Published online:    1988-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

Keywords: