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