The zero level set for a certain weak solution, with applications to the Bellman equations
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- by J. Andersson and H. Mikayelyan PDF
- Trans. Amer. Math. Soc. 365 (2013), 2297-2316 Request permission
Abstract:
We will prove a partial regularity result for the zero level set of weak solutions to \[ \textrm {div}(B\nabla u)=0, \] 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
- MR Author ID: 683643
- Received by editor(s): June 28, 2010
- Received by editor(s) in revised form: February 24, 2011
- Published electronically: November 7, 2012
- © Copyright 2012 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 365 (2013), 2297-2316
- MSC (2010): Primary 35R35, 35J60, 35B65
- DOI: https://doi.org/10.1090/S0002-9947-2012-05593-0
- MathSciNet review: 3020099