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Regularity Theory of Elliptic and Parabolic Equations and Systems

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Year:
2017
Contributor:
Zhang, Hong (creator)
Dong, Hongjie (Advisor)
Guo, Yan (Reader)
Dafermos, Constantine (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Applied mathematics
Differential equations, Elliptic
Differential equations, Parabolic
Extent:
, None p.
DOI
https://doi.org/10.7301/Z06D5RGB

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Abstract:
In 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.
Notes:
Thesis (Ph. D.)--Brown University, 2017

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Citation

Zhang, Hong, "Regularity Theory of Elliptic and Parabolic Equations and Systems" (2017). Applied Mathematics Theses and Dissertations. Brown Digital Repository. Brown University Library. https://doi.org/10.7301/Z06D5RGB

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