Article ID Journal Published Year Pages File Type
840378 Nonlinear Analysis: Theory, Methods & Applications 2013 7 Pages PDF
Abstract

In R3R3, Lipschitz continuous viscosity solutions to the KK-prescribed Levi curvature equation are smooth and strictly pseudoconvex if KK is smooth and strictly positive; see [5]. We show here that in R2n+1R2n+1, n>1n>1, a similar result does not hold; that is, we prove the existence in Cn+1Cn+1, n>1n>1, of nonsmooth pseudoconvex hypersurfaces with smooth Levi curvature.

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