@misc{LokutsievskiyWachsmuthZelikin, author = {Lokutsievskiy, Lev and Wachsmuth, Gerd and Zelikin, Mikhail}, title = {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}, series = {arXiv}, journal = {arXiv}, pages = {1 -- 20}, abstract = {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.}, language = {en} } @misc{LokutsievskiyWachsmuthZelikin, author = {Lokutsievskiy, Lev and Wachsmuth, Gerd and Zelikin, Mikhail}, title = {Non-optimality of conical parts for Newton's problem of minimal resistance in the class of convex bodies}, series = {Calculus of Variations and Partial Differential Equations}, volume = {61}, journal = {Calculus of Variations and Partial Differential Equations}, number = {1}, issn = {1432-0835}, doi = {10.1007/s00526-021-02118-y}, language = {en} }