Boundary Value Problems in Lipschitz Domains for Equations with Drifts /

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Bibliographic Details
Author / Creator:	Sakellaris, Georgios, author.
Imprint:	2017. Ann Arbor : ProQuest Dissertations & Theses, 2017
Description:	1 electronic resource (230 pages)
Language:	English
Format:	E-Resource Dissertations
Local Note:	School code: 0330
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11715052

Hidden Bibliographic Details
Other authors / contributors:	University of Chicago. degree granting institution.
ISBN:	9780355077919
Notes:	Advisors: Carlos Kenig; Panagiotis Souganidis. Dissertation Abstracts International, Volume: 78-12(E), Section: B. English
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.

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