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    On the Lp-Integrability of Green’s function for Elliptic Operators

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    Type
    Thesis
    Authors
    Alharbi, Abdulrahman cc
    Advisors
    Gomes, Diogo A. cc
    Committee members
    Laleg-Kirati, Taous-Meriem cc
    Tzavaras, Athanasios cc
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2019-05-30
    Permanent link to this record
    http://hdl.handle.net/10754/655516
    
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    Abstract
    In this thesis, we discuss some of the results that were proven by Fabes and Stroock in 1984. Our main purpose is to give a self-contained presentation of the proof of this results. The first result is on the existence of a “reverse H ̈older inequality” for the Green’s function. We utilize the work of Muckenhoupt on the reverse Ho ̈lder inequality and its connection to the A∞ class to establish a comparability property for the Green’s functions. Additionally, we discuss some of the underlying preliminaries. In that, we prove the Alexandrov-Bakelman-Pucci estimate, give a treatment to the Ap and A∞ classes of Muckenhoupt, and establish two intrinsic lemmas on the behavior of Green’s function.
    Citation
    Alharbi, A. (2019). On the Lp-Integrability of Green’s function for Elliptic Operators. KAUST Research Repository. https://doi.org/10.25781/KAUST-71531
    DOI
    10.25781/KAUST-71531
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-71531
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; MS Theses; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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