manuscripta mathematica

, Volume 47, Issue 1–3, pp 133–151 | Cite as

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

  • Gunnar Aronsson


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.


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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

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

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