I solved it here is my solution:
U = reshape(x, [n,n]);
u1 = [zeros([1,n]); diff(U, 1, 1)];
u2 = [zeros(n, 1), diff(U, 1, 2)];
y = [u1(:); u2(:)];
To solved for we solve the equavalent formulation :
x1vec = x(1:end/2);
x2vec = x(end/2+1:end);
x1mat = reshape(x1vec, [n,n]);
x2mat = reshape(x2vec, [n,n]);
p1 = -diff(x1mat, 1, 1);
p1 = [-x1mat(2, :); p1(2:end,:); x1mat(end,:)];
p1 = p1(:);
p2 = -diff(x2mat, 1, 2);
p2 = [-x2mat(:,2), p2(:, 2:end), x2mat(:,end)];
p2 = p2(:);
y = p1+p2;