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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Linearly approximatable functions


Authors: Thierry De Pauw and Amos Koeller
Journal: Proc. Amer. Math. Soc. 137 (2009), 1347-1356
MSC (2000): Primary 26B35, 26B10, 46E10
Published electronically: October 6, 2008
MathSciNet review: 2465658
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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.


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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: http://dx.doi.org/10.1090/S0002-9939-08-09667-6
PII: S 0002-9939(08)09667-6
Received by editor(s): April 10, 2008
Published electronically: October 6, 2008
Additional Notes: The first author is a chercheur qualifié of the Fonds National de la Recherche Scientifique, Belgium
Communicated by: Tatiana Toro
Article copyright: © Copyright 2008 American Mathematical Society