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dc.contributor.advisorGomes, Diogo A.en_US
dc.contributor.authorAlharbi, Abdulrahmanen_US
dc.date.accessioned2019-06-11T10:38:47Z
dc.date.available2019-06-11T10:38:47Z
dc.date.issued2019-05-30
dc.identifier.doi10.25781/KAUST-71531
dc.identifier.urihttp://hdl.handle.net/10754/655516
dc.description.abstractIn 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.en_US
dc.language.isoenen
dc.subjectGreen's Functionsen_US
dc.subjectnon-divergence formen_US
dc.subjectFabes-Stroocken_US
dc.subjectABP Estimateen_US
dc.subjectMuckenhoupt Weightsen_US
dc.titleOn the Lp-Integrability of Green’s function for Elliptic Operatorsen_US
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen_US
thesis.degree.grantorKing Abdullah University of Science and Technologyen
dc.contributor.committeememberLaleg-Kirati, Taous-Meriemen_US
dc.contributor.committeememberTzavaras, Athanasiosen_US
thesis.degree.disciplineApplied Mathematics and Computational Scienceen_US
thesis.degree.nameMaster of Scienceen
refterms.dateFOA2019-06-11T10:38:48Z
kaust.request.doiyes


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