If the (direct) utility is concave in all goods, is the indirect utility necessarily concave in wealth? Suppose that the direct utility $u(x_1,...,x_n)$ is concave in each of its arguments.  Does this imply that the indirect utility $U(w,p)$ is concave with respect to $w$? If all goods are normal than this can proved. e.g. using Lagrange multipliers.  But, is it true in general?  

One can assume that $u$ is differential as many times as necessary.

Thanks.
Your statement does not seem to be true for normal goods either. A counterexample:
$$
U(x_1,x_2) = (x_1x_2)^{\frac{2}{3}}
$$
By the Cobb-Douglas property the optimum bundle given $w,p$ is
$$
(x_1,x_2) = \left(\frac{w}{2p_1}, \frac{w}{2p_2}\right),
$$
so both goods are normal. The indirect utility is
$$
U(w,p) = \left(\frac{1}{4p_1p_2}\right)^{\frac{2}{3}}w^{\frac{4}{3}}.
$$
Here $w$ is raised to a power higher than 1 so $U(w,p)$ is convex in $w$.