# Biharmonic equation with only zero normal derivative

**URL:** <https://community.freefem.org/t/biharmonic-equation-with-only-zero-normal-derivative/2835>\
**Category:** General Discussion\
**Created:** [December 14, 2023, 12:23am UTC](https://community.freefem.org/t/biharmonic-equation-with-only-zero-normal-derivative/2835 "2023-12-14T00:23:49Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![jvellojin](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/jvellojin/32/526_2.png) [@jvellojin](https://community.freefem.org/u/jvellojin)\
**Post date:** [December 14, 2023, 12:23am UTC](https://community.freefem.org/t/biharmonic-equation-with-only-zero-normal-derivative/2835/1 "2023-12-14T00:23:49Z")

</div>

Dear Freefem community,

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

```auto
load "Morley"
// Parameters
int nn = 10; real h = 0.01;
real f = 1;
// Mesh
mesh Th = square(nn, nn);
Th = adaptmesh(Th, h, IsMetric=1);
// 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!

---

<div class="post-metadata">

**Author:** ![lassounon](https://avatars.discourse-cdn.com/v4/letter/l/bbe5ce/32.png) [@lassounon](https://community.freefem.org/u/lassounon)\
**Post date:** [December 15, 2023, 12:11pm UTC](https://community.freefem.org/t/biharmonic-equation-with-only-zero-normal-derivative/2835/2 "2023-12-15T12:11:01Z")

</div>

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](https://github.com/FreeFem/FreeFem-sources/blob/develop/examples/hpddm/bilaplace-2d-PETSc.edp)