  We develop a new approach and employ it to establish the global existence and
nonlinear structural stability of attached weak transonic shocks in steady
potential flow past three-dimensional wedges; in particular, the restriction
that the perturbation is away from the wedge edge in the previous results is
removed. One of the key ingredients is to identify a "good" direction of the
boundary operator of a boundary condition of the shock along the wedge edge,
based on the non-obliqueness of the boundary condition for the weak shock on
the edge. With the identification of this direction, an additional boundary
condition on the wedge edge can be assigned to make sure that the shock is
attached on the edge and linearly stable under small perturbation. Based on the
linear stability, we introduce an iteration scheme and prove that there exists
a unique fixed point of the iteration scheme, which leads to the global
existence and nonlinear structural stability of the attached weak transonic
shock. This approach is based on neither the hodograph transformation nor the
spectrum analysis, and should be useful for other problems with similar
difficulties.
