# Nonlinear orthogonal projection

Annales Polonici Mathematici (1994)

- Volume: 59, Issue: 1, page 1-31
- ISSN: 0066-2216

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topEwa Dudek, and Konstanty Holly. "Nonlinear orthogonal projection." Annales Polonici Mathematici 59.1 (1994): 1-31. <http://eudml.org/doc/262397>.

@article{EwaDudek1994,

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.},

author = {Ewa Dudek, Konstanty Holly},

journal = {Annales Polonici Mathematici},

keywords = {projection's regularity and interior of its domain; regularity; metric space; orthogonal projection; euclidean space; local Lipschitz condition},

language = {eng},

number = {1},

pages = {1-31},

title = {Nonlinear orthogonal projection},

url = {http://eudml.org/doc/262397},

volume = {59},

year = {1994},

}

TY - JOUR

AU - Ewa Dudek

AU - Konstanty Holly

TI - Nonlinear orthogonal projection

JO - Annales Polonici Mathematici

PY - 1994

VL - 59

IS - 1

SP - 1

EP - 31

AB - 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.

LA - eng

KW - projection's regularity and interior of its domain; regularity; metric space; orthogonal projection; euclidean space; local Lipschitz condition

UR - http://eudml.org/doc/262397

ER -

## References

top- [1] E. Asplund, Čebyšev sets in Hilbert space, Trans. Amer. Math. Soc. 144 (1969), 235-240. Zbl0187.05504
- [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). Zbl0095.08903
- [5] H. Federer, Curvature measures, Trans. Amer. Math. Soc. 93 (1959), 418-491. Zbl0089.38402
- [6] D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977. Zbl0361.35003
- [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. Zbl0091.27701
- [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. Zbl0011.41105
- [15] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1974. Zbl0278.26001
- [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. Zbl0181.38003

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