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Range of the gradient of a smooth bump function in finite dimensions
Author(s):
Ludovic
Rifford
Journal:
Proc. Amer. Math. Soc.
131
(2003),
3063-3066.
MSC (2000):
Primary 46G05, 58C25
Posted:
March 11, 2003
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Abstract:
This paper proves the semi-closedness of the range of the gradient for sufficiently smooth bumps in the Euclidean space.
References:
-
- 1.
- J. M. Borwein, M. Fabian, I. Kortezov, and P. D. Loewen.
The range of the gradient of a continuously differentiable bump.
J. Nonlinear Convex Anal., 2(1):1-19, 2001. MR 2002c:58012 - 2.
- H. Federer.
Geometric measure theory.
Springer-Verlag, New York Inc., New York, 1969. MR 41:1976 - 3.
- T. Gaspari.
On the range of the derivative of a real valued function with bounded support.
Preprint. - 4.
- W. Rudin.
Principles of mathematical analysis.
McGraw-Hill Book Co., New York, 1964. MR 29:3587 - 5.
- M. Spivak.
A comprehensive introduction to differential geometry. Vol. I.
Publish or Perish Inc., Wilmington, Del., second edition, 1979. MR 82g:53003a - 6.
- X. Wang.
Pathological examples of Lipschitz functions.
Ph.D. thesis, SFU, 1995.
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Additional Information:
Ludovic
Rifford
Affiliation:
Institut Girard Desargues, Université Claude Bernard Lyon I, 69622 Villeurbanne, France
Email:
rifford@igd.univ-lyon1.fr
DOI:
10.1090/S0002-9939-03-07078-3
PII:
S 0002-9939(03)07078-3
Keywords:
Smooth bump,
gradient
Received by editor(s):
April 16, 2002
Posted:
March 11, 2003
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2003,
American Mathematical Society
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