|
Linearly approximatable functions
Author(s):
Thierry
De Pauw;
Amos
Koeller
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1347-1356.
MSC (2000):
Primary 26B35, 26B10, 46E10
Posted:
October 6, 2008
MathSciNet review:
2465658
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
The notion of uniform linear approximatability generalizes that of being continuously differentiable. It occurs, e.g., in viscosity solutions of some degenerate partial differential equations. We establish the Hölder continuity of uniformly linearly approximatable functions, and we show that functions which are nowhere linearly approximatable form a residual collection of the appropriate Hölder space. Finally, we prove an analog of the implicit function theorem applied to level sets.
References:
-
- 1.
- G. Aronsson, M.G. Crandall, and P. Juutinen, A tour of the theory of absolutely minimizing functions, Bull. Amer. Math. Soc. 41 (2004), no. 4, 439-505. MR 2083637 (2005k:35159)
- 2.
- S. Banach, Über die bairesche kategorie gewisser funktionenmengen, Stud. Math. 3 (1931), 174-179.
- 3.
- M.G. Crandall and L.C. Evans, A remark on infinity harmonic functions, Electron. J. Diff. Eqns. Conf. 06 (2001), 123-129. MR 1804769 (2001j:35076)
- 4.
- G. David, Th. De Pauw, and T. Toro, Extensions of Reifenberg's topological disk theorem, Geom. Funct. Anal. (to appear).
- 5.
- Th. De Pauw and P. Huovinen, Points of
 -differentiability of Lipschitz functions from  to  , Bull. London Math. Soc. 34 (2002), 539-550. MR 1912876 (2003f:26014) - 6.
- F. Grünbaum and E.H. Zarantonello, On the extension of uniformly continuous mappings, Michigan Math. J. 15 (1968), 65-74. MR 0223506 (36:6554)
- 7.
- S. Mazurkiewicz, Sur les fonctions non dérivables, Stud. Math 3 (1931), 92-94.
- 8.
- C.B. Morrey Jr., Multiple integrals in the calculus of variations, Springer, 1966. MR 0202511 (34:2380)
- 9.
- E.R. Reifenberg, Solution of the Plateau problem for m-dimensional surfaces of varying topological type, Acta Math. 104 (1960), 1-92. MR 0114145 (22:4972)
- 10.
- O. Savin,
 regularity for infinity harmonic functions in two dimensions, Arch. Ration. Mech. Anal. 176 (2005), 351-361. MR 2185662 (2006i:35108) - 11.
- T. Toro, Geometric conditions and existence of bi-Lipschitz parameterizations, Duke Math. J. 77 (1995), no. 1, 193-227. MR 1317632 (96b:28006)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
26B35, 26B10, 46E10
Retrieve articles in all Journals with
MSC (2000):
26B35, 26B10, 46E10
Additional Information:
Thierry
De Pauw
Affiliation:
Université Catholique de Louvain, Département de Mathématiques, Chemin du Cyclotron, 2, B-1348 Louvain-la-Neuve, Belgique
Email:
thierry.depauw@uclouvain.be
Amos
Koeller
Affiliation:
Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
Email:
akoeller@everest.mathematik.uni-tuebingen.de
DOI:
10.1090/S0002-9939-08-09667-6
PII:
S 0002-9939(08)09667-6
Received by editor(s):
April 10, 2008
Posted:
October 6, 2008
Additional Notes:
The first author is a {\em chercheur qualifié of the {\em Fonds National de la Recherche Scientifique}, Belgium
Communicated by:
Tatiana Toro
Copyright of article:
Copyright
2008,
American Mathematical Society
|
