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Transactions of the American Mathematical Society

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Weakly coupled systems of the infinity Laplace equations


Authors: H. Mitake and H. V. Tran
Journal: Trans. Amer. Math. Soc. 369 (2017), 1773-1795
MSC (2010): Primary 35D40, 35J47, 35J70; Secondary 49L20
DOI: https://doi.org/10.1090/tran6694
Published electronically: May 6, 2016
MathSciNet review: 3581219
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Abstract: We derive the weakly coupled systems of the infinity Laplace equations via a tug-of-war game introduced by Peres, Schramm, Sheffield, and Wilson (2009). We establish existence, uniqueness results of the solutions, and introduce a new notion of ``generalized cones'' for systems. By using ``generalized cones'' we analyze blow-up limits of solutions.


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Additional Information

H. Mitake
Affiliation: Institute for Sustainable Sciences and Development, Hiroshima University 1-4-1 Kagamiyama, Higashi-Hiroshima-shi 739-8527, Japan
Email: hiroyoshi-mitake@hiroshima-u.ac.jp

H. V. Tran
Affiliation: Department of Mathematics, The University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
Email: hung@math.uchicago.edu

DOI: https://doi.org/10.1090/tran6694
Keywords: Infinity Laplace equations, comparison with cones, tug-of-war, piecewise-deterministic Markov processes, weakly coupled systems, viscosity solutions
Received by editor(s): April 14, 2014
Received by editor(s) in revised form: March 6, 2015
Published electronically: May 6, 2016
Additional Notes: The work of the first author was partially supported by the JST program to disseminate tenure tracking system, and JSPS KAKENHI #24840042.
Article copyright: © Copyright 2016 American Mathematical Society

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