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The p-Laplace equation  $$ \n \cdot (|\n u|^n \n u)=0 \whereA n>0, $$ in a bounded domain $\O \subset\re^2$, with inhomogeneous Dirichlet conditions on the smooth boundary $\p \O$is considered. In addition, there is a finite collection of curves  $$\Gamma = \Gamma_1\cup...\cup\Gamma_m \subset \O, \quad \{on which we assumehomogeneous Dirichlet boundary conditions} \quad u=0, $$ modeling a multiplecrack formation, focusing at the origin $0 \in \O$. This makes the abovequasilinear elliptic problem overdetermined. Possible types of the behaviour ofsolution $u(x,y)$ at the tip 0 of such admissible multiple cracks, being a"singularity" point, are described, on the basis of blow-up scaling techniquesand a "nonlinear eigenvalue problem". Typical types of admissible cracks areshown to be governed by nodal sets of a countable family of nonlineareigenfunctions, which are obtained via branching from harmonic polynomials thatoccur for $n=0$. Using a combination of analytic and numerical methods,saddle-node bifurcations in $n$ are shown to occur for those nonlineareigenvalues/eigenfunctions.

The p-Laplace equation in domains with multiple crack section via pencil operators