On the local Hölder continuity of the inverse of the $p$-Laplace operator
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Abstract:
We prove an interpolation type inequality between $C^\alpha$, $L^\infty$ and $L^p$ spaces and use it to establish the local Hölder continuity of the inverse of the $p$-Laplace operator: $\|(-\Delta _p)^{-1}(f) - (-\Delta _p)^{-1}(g)\|_{C^{1}(\bar {\Omega })} \leq C \| f - g \|^r_{L^\infty (\Omega )}$, for any $f$ and $g$ in a bounded set in $L^\infty (\Omega )$.References
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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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3553-3560
- MSC (2000): Primary 35J60, 35B65; Secondary 46B70
- DOI: https://doi.org/10.1090/S0002-9939-07-08913-7
- MathSciNet review: 2336570