论文标题
牛顿在凸形体类别中最小电阻的问题的圆锥形零件和无限高度的极限情况
Non-optimality of conical parts for Newton's problem of minimal resistance in the class of convex bodies and the limiting case of infinite height
论文作者
论文摘要
我们考虑了牛顿的最小阻力问题，特别是我们解决了如果高度到达无穷大，则在限制中产生的问题。我们建立了解决方案的存在，并且缺乏解决方案的径向对称性。此外，我们表明，凸体边界中包含的某些圆锥形部件抑制了经典牛顿的最佳性质，并具有有限的高度。该结果应用于文献中考虑的某些物体，这些物体对经典牛顿的问题是最佳的，我们表明它们不是。
We consider Newton's problem of minimal resistance, in particular we address the problem arising in the limit if the height goes to infinity. We establish existence of solutions and lack radial symmetry of solutions. Moreover, we show that certain conical parts contained in the boundary of a convex body inhibit the optimality in the classical Newton's problem with finite height. This result is applied to certain bodies considered in the literature, which are conjectured to be optimal for the classical Newton's problem, and we show that they are not.
