Typical boundary conditions for elliptic and parabolic PDEs involve
derivatives normal to the boundaries (
), i.e. flux components normal
to the boundaries (3.3-58).
Here, 
stands for an arbitrary function of 
. In our case the
boundary is represented by equicoordinate lines. The contravariant base
vectors 
and 
are normal to the equicoordinate lines, and
therefore the flux component normal to the boundary is given by
(3.3-59) and (3.3-60) for boundaries
and 
, respectively.
