Applying several BC to a boundary

Hi there;

I wonder if anyone can help me find out how I can apply several derivatives in a boundary; in a 1D problem
\frac{\partial \phi}{\partial x}=\alpha
\frac{\partial^2 \phi}{\partial x^2}=\beta
\frac{\partial^3 \phi}{\partial x^3}=\gamma
How can I impose them to a single boundary?
And does it make sense? If so, is there any consideration on the element type that should be used?

You have to write the correct variationnal form of you problem, I thing it is a Tri-Laplacien , this imply C^2 conformity and we do not have is regularity on FreeFEM++ finite element.