  In this paper we consider a minimization problem for the functional $$
J(u)=\int_{B_1^+}|\nabla u|\sp
2+\lambda_{+}^2\chi_{\{u>0\}}+\lambda_{-}^2\chi_{\{u\leq0\}}, $$ in the upper
half ball $B_1^+\subset\R^n, n\geq 2$ subject to a Lipschitz continuous
Dirichlet data on $\partial B_1^+$. More precisely we assume that $0\in
\partial \{u>0\}$ and the derivative of the boundary data has a jump
discontinuity. If $0\in \bar{\partial(\{u>0\} \cap B_1^+)}$ then (for $n=2$ or
$n>3$ and one-phase case) we prove, among other things, that the free boundary
$\partial \{u>0\}$ approaches the origin along one of the two possible planes
given by $$ \gamma x_1 = \pm x_2, $$ where $\gamma$ is an explicit constant
given by the boundary data and $\lambda_\pm$ the constants seen in the
definition of $J(u)$. Moreover the speed of the approach to $\gamma x_1=x_2$ is
uniform.

Analysis of PDEs