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    The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases

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    Type
    Article
    Authors
    Gomes, Diogo A. cc
    Mitake, Hiroyoshi
    Tran, Hung V.
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Date
    2018-01-26
    Online Publication Date
    2018-01-26
    Print Publication Date
    2018-01
    Permanent link to this record
    http://hdl.handle.net/10754/627149
    
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    Abstract
    Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton–Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex Hamiltonians has thus far not been studied. We begin our study by examining a generalized discounted Hamilton–Jacobi equation. Next, using an exponential transformation, we apply our methods to strictly quasi-convex and to some non-convex Hamilton–Jacobi equations. Finally, we examine a non-convex Hamiltonian with flat parts to which our results do not directly apply. In this case, we establish the convergence by a direct approach.
    Citation
    GOMES DA, MITAKE H, TRAN HV (2018) The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases. Journal of the Mathematical Society of Japan 70: 345–364. Available: http://dx.doi.org/10.2969/jmsj/07017534.
    Publisher
    Mathematical Society of Japan (Project Euclid)
    Journal
    Journal of the Mathematical Society of Japan
    DOI
    10.2969/jmsj/07017534
    arXiv
    1605.07532
    Additional Links
    https://projecteuclid.org/euclid.jmsj/1516957230#info
    ae974a485f413a2113503eed53cd6c53
    10.2969/jmsj/07017534
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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