Existence of minimizers for Newton's problem of the body of minimal resistance under a single impact assumption

Abstract

We prove that the infimum of Newton's functional of minimal resistanceF(u):=∫_Ω dx/(1+|▽u(x)|²), where Ω ⊂R ² is a strictly convex domain, is not attained in a wide class of functions satisfying a single-impact assumption, proposed in [1]. On the other hand, we prove that the infimum is attained in the subclass of radial functions; hence the minimizers are the local minimizers already described in [3].