Non-Removable Singularities of a Fourth Order Nonlinear Partial Differential Equation
2009 - J.A. Aledo, A. Martínez, F. Milán.
Journal of Differential Equations 247, 331-343 (2009)
The aim of this paper is to give a classification of the solutions =(x,y) of the fourth-order nonlinear equation yy?xx?2xy?xy+xx?yy=0, ?=(det(2))?3/4, in a punctured domain which are at the singularity. We prove that this kind of solutions either have a removable singularity or are asymptotic to rotationally symmetric solutions near the singularity. A geometric description of solutions which are not at the singularity is also given.