On the local Hölder continuity of the inverse of the -Laplace operator
Author:
An Lê
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
Published electronically:
June 21, 2007
MathSciNet review:
2336570
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We prove an interpolation type inequality between ,
and
spaces and use it to establish the local Hölder continuity of the inverse of the
-Laplace operator:
, for any
and
in a bounded set in
.
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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:
https://doi.org/10.1090/S0002-9939-07-08913-7
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.