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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 regularity of solutions of the inhomogeneous infinity Laplace equation


Author: Erik Lindgren
Journal: Proc. Amer. Math. Soc. 142 (2014), 277-288
MSC (2010): Primary 49N60; Secondary 35J20, 35J65
Published electronically: October 2, 2013
MathSciNet review: 3119202
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Abstract: We study the inhomogeneous infinity Laplace equation and prove that for bounded and continuous inhomogeneities, any blow-up is linear but not necessarily unique. If, in addition, the inhomogeneity is assumed to be $ C^1$, then we prove that any solution is differentiable, i.e., that any blow-up is unique.


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Additional Information

Erik Lindgren
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, Alfred Getz vei 1, NO-7491 Trondheim, Norway
Address at time of publication: Department of Mathematics, KTH, S-100 44 Stockholm, Sweden
Email: erik.lindgren@math.ntnu.no

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-12180-5
Received by editor(s): April 22, 2011
Received by editor(s) in revised form: March 8, 2012
Published electronically: October 2, 2013
Communicated by: James E. Colliander
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.