# Biharmonic equation with only zero normal derivative

Dear Freefem community,

I’m trying to manipulate the boundary conditions for the bilaplacian problem, like the code below.

``````load "Morley"
// Parameters
int nn = 10; real h = 0.01;
real f = 1;
// Mesh
mesh Th = square(nn, nn);
// Fespace
fespace Vh(Th, P2Morley); //The Morley finite element space

Vh [u, ux, uy], [v, vx, vy];
// Macro
macro bilaplacien(u, v) (dxx(u)*dxx(v) + dyy(u)*dyy(v) + 2.*dxy(u)*dxy(v)) //
// Problem
solve bilap ([u, ux, uy], [v, vx, vy]) = int2d(Th)(
bilaplacien(u, v)
)
- int2d(Th)(
f*v
)
+ on(1, 2, 3, 4, u=0, ux=0, uy=0)
;
// Plot
plot(u, cmm="u");

``````

I’m wondering if is possible to remove the boundary condition u=0 and let only ux=uy=0. I tried `on(1, 2, 3, 4, ux=0, uy=0)` with no luck.

Any help is appreciated and thanks in advance!

An example is in the Freefem++ documentation, page 307 for Morley finite elements and you will see how the boundary conditions are taken into account https://github.com/FreeFem/FreeFem-sources/blob/develop/examples/hpddm/bilaplace-2d-PETSc.edp