Regularity Theory of Elliptic and Parabolic Equations and SystemsZhang, HongcreatorDong, HongjieAdvisorGuo, YanReaderDafermos, ConstantineReaderBrown University. Department of Applied Mathematicssponsor2017, None p.born digitalThesis (Ph. D.)--Brown University, 2017thesesIn this dissertation, we study regularity theory of elliptic and parabolic equations and systems with irregular coefficients. In the first part of the dissertation, we consider Schauder and Lp theories for general linear elliptic and parabolic systems with particular types of irregular coefficients. We also establish some new regularity results regarding a model from the fiber reinforced composite material and expand the Lp and Schauder estimates of higher-order parabolic equations and systems to include a large class of irregular coefficients. In the second part of the dissertation, we investigate the regularity problem of nonlinear nonlocal elliptic and parabolic equations. We prove the Schauder estimates for concave fully nonlinear nonlocal parabolic equations and then establish the Dini type estimates for such type of equations.Applied mathematicsDifferential equations, EllipticDifferential equations, ParabolicEnglishRPB2017061610.7301/Z06D5RGBIn CopyrightCollection is open for research.dissertations