Let
D
D
be a plane domain partly bounded by two line segments which meet at the origin and form there an interior angle
π
α
>
0
\pi \alpha > 0
. Let
U
(
x
,
y
)
U(x,y)
be a solution in
D
D
of Poisson’s equation such that either
U
U
or
∂
U
/
∂
n
\partial U/\partial n
(the normal derivative) takes prescribed values on the boundary segments. Let
U
(
x
,
y
)
U(x,y)
be sufficiently smooth away from the corner and bounded at the corner. Then for each positive integer
N
N
there exists a function
V
N
(
x
,
y
)
{V_N}(x,y)
which satisfies a related Poisson equation and which satisfies related boundary conditions such that
U
−
V
N
U - {V_N}
is
N
N
-times continuously differentiable at the corner. If
1
/
α
1/\alpha
is an integer
V
N
{V_N}
may be found explicitly in terms of the data of the problem for
U
U
.