Nonlinear orthogonal projection

• Autorzy: Ewa Dudek , Konstanty Holly
• Języki publikacji: EN

Abstrakty

EN

We discuss some properties of an orthogonal projection onto a subset of a Euclidean space. The special stress is laid on projection's regularity and characterization of the interior of its domain.

Słowa kluczowe

EN

projection's regularity and interior of its domain

Kategorie tematyczne

• 58B10: Differentiability questions
• 51Kxx: Distance geometry

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994
• Tom: 59
• Numer: 1
• Strony: 1-31

Daty

wydano

1994

otrzymano

1991-06-28

poprawiono

1993-01-04

Twórcy

autor

Ewa Dudek

• Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

autor

Konstanty Holly

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

• [1] E. Asplund, Čebyšev sets in Hilbert space, Trans. Amer. Math. Soc. 144 (1969), 235-240.
• [2] L. N. H. Bunt, Contributions to the theory of convex point sets, Ph.D. Thesis, Groningen, 1934 (in Dutch).
• [3] E. Dudek, Orthogonal projection onto a subset of a Euclidean space, Master's thesis, Kraków, 1989 (in Polish).
• [4] N. V. Efimov and S. B. Stechkin, Support properties of sets in Banach spaces and Chebyshev sets, Dokl. Akad. Nauk SSSR 127 (1959), 254-257 (in Russian).
• [5] H. Federer, Curvature measures, Trans. Amer. Math. Soc. 93 (1959), 418-491.
• [6] D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977.
• [7] M. W. Hirsch, Differential Topology, Springer, New York, 1976.
• [8] E. Hopf, On non-linear partial differential equations, in: Lecture Series of the Symposium on Partial Diff. Equations, Berkeley, 1955, The Univ. of Kansas, 1957, 1-29.
• [9] G. Jasiński, A characterization of the differentiable retractions, Univ. Iagell. Acta Math. 26 (1987), 99-103.
• [10] V. L. Klee, Convexity of Chebyshev sets, Math. Ann. 142 (1961), 292-304.
• [11] V. L. Klee, Remarks on nearest points in normed linear spaces, in: Proc. Colloquium on Convexity (Copenhagen, 1965), Kobenhavns Univ. Mat. Inst., Copenhagen, 1967, 168-176.
• [12] S. G. Krantz and H. R. Parks, Distance to $C^k$ hypersurfaces, J. Differential Equations 40 (1981), 116-120.
• [13] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod and Gauthier-Villars, Paris, 1969.
• [14] T. Motzkin, Sur quelques propriétés caractéristiques des ensembles convexes, Atti R. Accad. Lincei Rend. (6) 21 (1935), 562-567.
• [15] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1974.
• [16] J. Serrin, The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables, Philos. Trans. Roy. Soc. London Ser. A 264 (1969), 413-496.