ArticleOriginal scientific text

Title

Nonlinear orthogonal projection

Authors 1, 2

Affiliations

  1. Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland
  2. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Abstract

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.

Keywords

projection's regularity and interior of its domain

Bibliography

  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 Ck 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.
Pages:
1-31
Main language of publication
English
Received
1991-06-28
Accepted
1993-01-04
Published
1994
Exact and natural sciences