manuscripta mathematica

, Volume 47, Issue 1, pp 133–151

On certain singular solutions of the partial differential equation ux2uxx+2uxuyuxy+uy2uyy=0

  • Gunnar Aronsson

DOI: 10.1007/BF01174590

Cite this article as:
Aronsson, G. Manuscripta Math (1984) 47: 133. doi:10.1007/BF01174590


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.

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Gunnar Aronsson
    • 1
  1. 1.Department of MathematicsUniversity of LuleåLuleåSweden