, Volume 47, Issue 1-3, pp 133-151

On certain singular solutions of the partial differential equation u x 2 uxx+2uxuyuxy+u y 2 uyy=0

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Abstract

The partial differential equation treated here is the formal limit of the p-harmonic equation in R2, for p→∞. Questions related to the smoothness of solutions and the possible existence of stationary points are central for the theory. The “singular” solutions constructed here bring new light on these questions.