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

 

On the local Hölder continuity of the inverse of the $ p$-Laplace operator


Author: An Lê
Journal: Proc. Amer. Math. Soc. 135 (2007), 3553-3560
MSC (2000): Primary 35J60, 35B65; Secondary 46B70
Published electronically: June 21, 2007
MathSciNet review: 2336570
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Abstract: We prove an interpolation type inequality between $ C^\al$, $ L^\infty$ and $ L^p$ spaces and use it to establish the local Hölder continuity of the inverse of the $ p$-Laplace operator: $ \Vert(-\Delta_p)^{-1}(f) - (-\Delta_p)^{-1}(g)\Vert _{C^{1}(\bar{\Omega})} \leq C \Vert f - g \Vert^r_{L^\infty(\Om)}$, for any $ f$ and $ g$ in a bounded set in $ L^\infty(\Omega)$.


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Additional Information

An Lê
Affiliation: Mathematics Sciences Research Institute, 17 Gauss Way, Berkeley, California 794720
Address at time of publication: Department of Mathematics and Statistics, Utah State University, 3900 Old Main Hill, Logan, Utah 84322
Email: anle@cc.usu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08913-7
PII: S 0002-9939(07)08913-7
Keywords: $p$-Laplace operator, interpolation inequalities, H\"{o}lder continuity
Received by editor(s): December 1, 2005
Received by editor(s) in revised form: August 4, 2006
Published electronically: June 21, 2007
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.