chebop2 for a biharmonic problem

[nickhale]

When I try to solve the following biharmonic problem, chebop2 returns a result which seems reasonable, but is actually far from a solution to the problem:

N = chebop2(@(u) diffx(u,4) + 2*diffy(diffx(u,2),2) + diffy(u,4));
N.lbc = @(y,u) [u-y ; diff(u)];
N.rbc = @(y,u) [u-1/2*y.*(3-y.^2) ; diff(u)];
N.ubc = @(x,u) [u-1 ; diff(u)];
N.dbc = @(x,u) [u+1 ; diff(u)];
u = N\0;
norm(N(u))
ans =
   6.000000000011491

My suspicion is that this might be related to some incompatibility of the boundary conditions (u_y has a jump at (-1,+-1). However, my experience from 2nd-order problems ni chebop2 is that boundary conditions are usually ignored in favour of solving the PDE, for example:

N = chebop2(@(u) lap(u), [-1 1 -1 1]);
N.lbc = 1; N.dbc = 0; N.ubc = 0; N.rbc = 0;
u = N\0
figure
plot(u), shg

Clearly the boundary conditions aren't correct (although no warning is given.)