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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The zero level set for a certain weak solution, with applications to the Bellman equations


Authors: J. Andersson and H. Mikayelyan
Journal: Trans. Amer. Math. Soc. 365 (2013), 2297-2316
MSC (2010): Primary 35R35, 35J60, 35B65
Published electronically: November 7, 2012
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Abstract | References | Similar Articles | Additional Information

Abstract: We will prove a partial regularity result for the zero level set of weak solutions to

$\displaystyle \textrm {div}(B\nabla u)=0, $

where $ B=B(u)=I+(A-I)\chi _{\{u<0\}}$, where $ I$ is the identity matrix and the eigenvalues of $ A$ are strictly positive and bounded.

We will apply this to describe the regularity of solutions to the Bellman equations.


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Additional Information

J. Andersson
Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom

H. Mikayelyan
Affiliation: Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, 111 Ren’ai Road, 215123 Suzhou (SIP), Jiangsu Province, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05593-0
PII: S 0002-9947(2012)05593-0
Received by editor(s): June 28, 2010
Received by editor(s) in revised form: February 24, 2011
Published electronically: November 7, 2012
Article copyright: © Copyright 2012 American Mathematical Society