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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

   

 

Regularity theory for parabolic nonlinear integral operators


Authors: Luis Caffarelli, Chi Hin Chan and Alexis Vasseur
Journal: J. Amer. Math. Soc. 24 (2011), 849-869
MSC (2010): Primary 35B65, 45G05, 47G10
Published electronically: March 24, 2011
MathSciNet review: 2784330
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Abstract: This article is dedicated to the regularity theory for solutions to a class of nonlinear integral variational problems. Those problems are involved in nonlocal image and signal processing.


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Additional Information

Luis Caffarelli
Affiliation: Department of Mathematics, University of Texas at Austin, 1 University Station, C1200, Austin, Texas 78712

Chi Hin Chan
Affiliation: Institute for Mathematics and Its Applications, University of Minnesota, 207 Church Street SE, Minneapolis, MN 55455-0134

Alexis Vasseur
Affiliation: Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford, OX1 3LB England

DOI: http://dx.doi.org/10.1090/S0894-0347-2011-00698-X
Keywords: Nonlinear partial differential equation, nonlocal operators, integral variational problems, De Giorgi methods, image and signal processing.
Received by editor(s): March 8, 2010
Received by editor(s) in revised form: August 2, 2010, October 26, 2010, and December 17, 2010
Published electronically: March 24, 2011
Additional Notes: The first author was partially supported by the NSF
The third author was partially supported by both the NSF and the EPSRC Science and Innovation award to the Oxford Centre for Nonlinear PDE (EP/E035027/1)
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



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