Abstract
In this chapter, we introduce the main mathematical notation that will be used throughout the book and state the main results of the book. The proofs of these results are given in Chaps. 2 –9.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Personal communication.
References
Newton, I.: Philosophiae naturalis principia mathematica. London: Streater (1687)
Tikhomirov, V.M.: Newton’s aerodynamic problem. Kvant (5), 11–18 (1982) (in Russian)
Tikhomirov, V.M.: Stories about maxima and minima. In: Mathematical World, vol. 1. AMS, Providence (1990) [Translated from: V.M. Tikhomirov. Rasskazy o maksimumakh i minimumakh. Nauka, Moscow, 1986 (in Russian)]
Brock, F., Ferone, V., Kawohl, B.: A symmetry problem in the calculus of variations. Calc. Var. 4, 593–599 (1996)
Bucur, D., Buttazzo, G.: Variational Methods in Shape Optimization Problems. Progress in Nonlinear Differential Equations and Their Applications 65, Birkhäuser, Boston, Inc., Boston, MA (2005)
Buttazzo, G., Ferone, V., Kawohl, B.: Minimum problems over sets of concave functions and related questions. Math. Nachr. 173, 71–89 (1995)
Comte, M., Lachand-Robert, T.: Newton’s problem of the body of minimal resistance under a single-impact assumption. Calc. Var. Partial Differ. Eq. 12, 173–211 (2001)
Comte, M., Lachand-Robert, T.: Functions and domains having minimal resistance under a single-impact assumption. SIAM J. Math. Anal. 34, 101–120 (2002)
Lachand-Robert, T., Oudet, E. Minimizing within convex bodies using a convex hull method. SIAM J. Optim. 16, 368–379 (2006)
Lachand-Robert, T., Peletier, M.A.: An example of non-convex minimization and an application to Newton’s problem of the body of least resistance. Ann. Inst. H. Poincaré Anal. Non Lin. 18, 179–198 (2001)
Lachand-Robert, T., Peletier, M.A.: Newton’s problem of the body of minimal resistance in the class of convex developable functions. Math. Nachr. 226, 153–176 (2001)
Buttazzo, G., Kawohl, B.: On Newton’s problem of minimal resistance. Math. Intell. 15, 7–12 (1993)
McCann, R.J.: Exact solutions to the transportation problem on the line. Proc. R. Soc. Lond. A 455, 1341–1380 (1999)
Levin, V.L.: Optimal solutions of the Monge problem. Adv. Math. Econ. 6, 85–122 (2004)
Levin, V.L.: Solution of the Monge and the Monge–Kantorovich problems. Theory and applications. Dokl. Akad. Nauk 388, 7–10 (2003) (in Russian)
Uckelmann, L.: Optimal couplings between one-dimensional distributions. In: Benes, V., Stepan, J. (eds.) Distributions with Given Marginals and Moment Problems, pp. 275–281. Kluwer, Dordrecht (1997)
Borg, K.I., Söderholm, L.H., Essén, H.: Force on a spinning sphere moving in a rarefied gas. Phys. Fluids 15, 736–741 (2003)
Ivanov, S.G., Yanshin, A.M.: Forces and moments acting on bodies rotating around a symmetry axis in a free molecular flow. Fluid Dyn. 15, 449 (1980)
Wang, C.T.: Free molecular flow over a rotating sphere. AIAA J. 10, 713 (1972)
Weidman, P.D., Herczynski, A.: On the inverse Magnus effect in free molecular flow. Phys. Fluids 16, L9–L12 (2004)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media New York
About this chapter
Cite this chapter
Plakhov, A. (2012). Notation and Synopsis of Main Results. In: Exterior Billiards. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4481-7_1
Download citation
DOI: https://doi.org/10.1007/978-1-4614-4481-7_1
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-4480-0
Online ISBN: 978-1-4614-4481-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)