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.
@article{bwmeta1.element.bwnjournal-article-apmv59z1p1bwm, author = {Ewa Dudek and Konstanty Holly}, title = {Nonlinear orthogonal projection}, journal = {Annales Polonici Mathematici}, volume = {60}, year = {1994}, pages = {1-31}, zbl = {0812.51010}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv59z1p1bwm} }
Ewa Dudek; Konstanty Holly. Nonlinear orthogonal projection. Annales Polonici Mathematici, Tome 60 (1994) pp. 1-31. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv59z1p1bwm/
[000] [1] E. Asplund, Čebyšev sets in Hilbert space, Trans. Amer. Math. Soc. 144 (1969), 235-240. | Zbl 0187.05504
[001] [2] L. N. H. Bunt, Contributions to the theory of convex point sets, Ph.D. Thesis, Groningen, 1934 (in Dutch).
[002] [3] E. Dudek, Orthogonal projection onto a subset of a Euclidean space, Master's thesis, Kraków, 1989 (in Polish).
[003] [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). | Zbl 0095.08903
[004] [5] H. Federer, Curvature measures, Trans. Amer. Math. Soc. 93 (1959), 418-491. | Zbl 0089.38402
[005] [6] D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977. | Zbl 0361.35003
[006] [7] M. W. Hirsch, Differential Topology, Springer, New York, 1976.
[007] [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.
[008] [9] G. Jasiński, A characterization of the differentiable retractions, Univ. Iagell. Acta Math. 26 (1987), 99-103.
[009] [10] V. L. Klee, Convexity of Chebyshev sets, Math. Ann. 142 (1961), 292-304. | Zbl 0091.27701
[010] [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.
[011] [12] S. G. Krantz and H. R. Parks, Distance to hypersurfaces, J. Differential Equations 40 (1981), 116-120.
[012] [13] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod and Gauthier-Villars, Paris, 1969.
[013] [14] T. Motzkin, Sur quelques propriétés caractéristiques des ensembles convexes, Atti R. Accad. Lincei Rend. (6) 21 (1935), 562-567. | Zbl 0011.41105
[014] [15] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1974. | Zbl 0278.26001
[015] [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. | Zbl 0181.38003