Hello specialists in solving PDE's,

I have a boundary value problem with the biharmonic equation and I want solve it with

DSolve[]

After defining the equation, the boundary conditions and the region over that DSolve should solve,

BiPotEq = Laplacian[Laplacian[f[x, y], {x, y}], {x, y}] == 0;
BCOne = Derivative[0, 2][f][-a, y] == (-12*mBZ)/(t*b^3)*(y - b/2);
BCTwo = Derivative[0, 2][f][a, y] == (-12*mBZ)/(t*b^3)*(y - b/2);
BCThree = Derivative[1, 1][f][-a, y] == 0;
BCFour = Derivative[1, 1][f][a, y] == 0;
BCFive = Derivative[1, 1][f][x, 0] == (p*12)/(a^3*11)*x^2 + (p*12)/(
    a*11);
BCSix = Derivative[2, 0][f][x, 0] == 0;
region = Rectangle[{-a/2, a/2}, {0, b}];
DSolve[{BiPotEq, BCOne, BCTwo, BCThree, BCFour, BCFive, BCSix}, 
 f[x, y], {x, y} \[Element] region]

I wonder why Mathematica is not able to solve that boundary value problem. I take it that Mathematica can solve the problem easily but even after studying the documentation about DSolve I cannot find my fault in coding.

Has anybody a hint for me?

Regards,
Michael