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    Harnack Inequality for a class of Degenerate Elliptic Equations in Non-Divergence Form

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    Genre
    Thesis/Dissertation
    Date
    2018
    Author
    Abedin, Farhan
    Advisor
    Gutiérrez, Cristian E., 1950-
    Committee member
    Berhanu, Shiferaw
    Yang, Wei-shih, 1954-
    Futer, David
    Hynd, Ryan
    Department
    Mathematics
    Subject
    Mathematics
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/624
    
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    DOI
    http://dx.doi.org/10.34944/dspace/606
    Abstract
    We provide two proofs of an invariant Harnack inequality in small balls for a class of second order elliptic operators in non-divergence form, structured on Heisenberg vector fields. We assume that the coefficient matrix is uniformly positive definite, continuous, and symplectic. The first proof emulates a method of E. M. Landis, and is based on the so-called growth lemma, which establishes a quantitative decay of oscillation for subsolutions. The second proof consists in establishing a critical density property for non-negative supersolutions, and then invoking the axiomatic approach developed by Di Fazio, Gutiérrez and Lanconelli to obtain Harnack’s inequality.
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