The existence of a body of minimal resistance with prescribed volume is proved in the class of profiles which satisfy a two sided bound on the mean curvature

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  1. G. Buttazzo: Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman Res. Notes Math. Ser. 207, Longman, Harlow (1989).Google Scholar
  2. G. Buttazzo, V. Ferone, B. Kawohl: Minimum Problems Over Sets of Concave Functions and Related Questions, Math. Nachr. 173 (1995) 71–89.https://doi.org/10.1002/mana.19951730106Google Scholar
  3. G. Buttazzo, P. Guasoni: Shape optimization problems over classes of convex domains, J. Convex Analysis 4(2) (1997) 343–351.https://doi.org/10.68381/jca04019Google Scholar
  4. L. C. Evans, R. F. Gariepy: Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton (1992).Google Scholar
  5. E. Giusti: Minimal Surfaces and Functions of Bounded Variation, Birkhäuser MMA 80 (1977).Google Scholar
  6. A. Miele: Theory of Optimum Aerodynamic Shapes, Academic Press, New York (1965).Google Scholar
  7. F. Nicolai: Un Modello Variazionale per l’Ottimizzazione di Profili Aerodinamici, Degree Thesis, Pisa (1994).Google Scholar
  8. A. Wagner: A Remark on Newton’s Resistance Formula, ZAMM 79, No. 6 (1999) 423–427.https://doi.org/10.1002/(SICI)1521-4001(199906)79:6<423::AID-ZAMM423>3.0.CO;2-VGoogle Scholar

M. Belloni, A. Wagner. “Newton's Problem of Minimal Resistance in the Class of Bodies with Prescribed Volume.” Journal of Convex Analysis 10 (2003), No. 2, 491–500. https://doi.org/10.68381/jca1030