Newton’s Problem of Minimal Resistance in Lorentz–Minkowski Space

We extend Newton’s problem of minimal resistance to the Lorentz–Minkowski space. We derive the functional energy and determine the Euler–Lagrange equation. In contrast to the Euclidean case, this equation is quasilinear elliptic, and thus, a maximum principle holds in this context. We obtain the solutions of this equation via separation of variables. Furthermore, we find all radial solutions to the problem, which present conical singularities at the origin. We also analyze the Single Shock Condition.