Boundary Value Problems in Lipschitz Domains for Equations with Drifts /

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Bibliographic Details
Author / Creator:Sakellaris, Georgios, author.
Ann Arbor : ProQuest Dissertations & Theses, 2017
Description:1 electronic resource (230 pages)
Format: E-Resource Dissertations
Local Note:School code: 0330
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Other authors / contributors:University of Chicago. degree granting institution.
Notes:Advisors: Carlos Kenig; Panagiotis Souganidis.
Dissertation Abstracts International, Volume: 78-12(E), Section: B.
Summary:In this work we establish solvability and uniqueness for the D2 Dirichlet problem and the R2 Regularity problem for second order elliptic operators L = −div(A∇·) + b∇· in bounded Lipschitz domains, for which b is bounded, as well as their adjoint operators Lt = -div( At∇·) -div(b·). The methods that we use are estimates on harmonic measure, and the method of layer potentials.
The nature of our methods applied to D2 for L and R2 for Lt leads us to impose a specific size condition on div b in order to obtain solvability. On the other hand, we show that R 2 for L and D2 for Lt are uniquely solvable, only assuming that A is Lipschitz continuous (and not necessarily symmetric) and b is just bounded.