  The problem considered first by I. Newton (1687) consists in finding a
surface of the minimal frontal resistance in a parallel flow of non-interacting
point particles. The standard formulation assumes that the surface is convex
with a given convex base $\Omega$ and a bounded altitude. Newton found the
solution for surfaces of revolution. Without this assumption the problem is
still unsolved, although many important results have been obtained in the last
decades. We consider the problem to characterize the domains $\Omega$ for which
the flat surface gives a local minimum. We show that this problem can be
reduced to an inequality between $L_2$-norms of partial derivatives for
bivariate concave functions on a convex domain that vanish on the boundary. Can
the ratio between those norms be arbitrarily large? The answer depends on the
geometry of the domain. A complete criterion is derived, which also solves the
local minimality problem.
