  We consider multi-dimensional junction problems for first- and second-order
pde with Kirchoff-type Neumann boundary conditions and we show that their
generalized viscosity solutions are unique. It follows that any viscosity-type
approximation of the junction problem converges to a unique limit. The results
here are the first of this kind and extend previous work by the authors for
one-dimensional junctions. The proofs are based on a careful analysis of the
behavior of the viscosity solutions near the junction, including a blow-up
argument that reduces the general problem to a one-dimensional one. As in our
previous note, no convexity assumptions and control theoretic interpretation of
the solutions are needed.
