Weakly coupled systems of the infinity Laplace equations
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- by H. Mitake and H. V. Tran PDF
- Trans. Amer. Math. Soc. 369 (2017), 1773-1795 Request permission
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.References
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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
- MR Author ID: 824759
- 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
- 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.
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 1773-1795
- MSC (2010): Primary 35D40, 35J47, 35J70; Secondary 49L20
- DOI: https://doi.org/10.1090/tran6694
- MathSciNet review: 3581219