  We use the minimizing movement theory to study the gradient flow associated
with a non-regular relaxation of a geometric functional derived from the
Willmore energy. Thanks to the coarea formula, one can define a Willmore energy
on regular functions of L 1 (R d). This functional is extended to every L 1
function by taking its lower semi-continuous envelope. We study the flow
generated by this relaxed energy for radially non-increasing functions, i.e.
functions with balls as level sets. In the first part of the paper, we prove a
coarea formula for the relaxed energy of such functions. Then we show that the
flow consists on an erosion of the initial data. The erosion speed is given by
a first order ordinary equation.
