Linearly approximatable functions
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- by Thierry De Pauw and Amos Koeller PDF
- Proc. Amer. Math. Soc. 137 (2009), 1347-1356 Request permission
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
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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
- 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
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 1347-1356
- MSC (2000): Primary 26B35, 26B10, 46E10
- DOI: https://doi.org/10.1090/S0002-9939-08-09667-6
- MathSciNet review: 2465658