Boundary Value Problems in Lipschitz Domains for Equations with Drifts /
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| 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 |
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| 100 | 1 | |a Sakellaris, Georgios, |e author. | |
| 245 | 1 | 0 | |a Boundary Value Problems in Lipschitz Domains for Equations with Drifts / |c Georgios Sakellaris. |
| 260 | |c 2017. | ||
| 264 | 1 | |a Ann Arbor : |b ProQuest Dissertations & Theses, |c 2017 | |
| 300 | |a 1 electronic resource (230 pages) | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
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| 500 | |a Advisors: Carlos Kenig; Panagiotis Souganidis. | ||
| 502 | |b Ph.D. |c University of Chicago, Division of the Physical Sciences, Department of Mathematics |d 2017. | ||
| 510 | 4 | |a Dissertation Abstracts International, |c Volume: 78-12(E), Section: B. | |
| 520 | |a 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. | ||
| 520 | |a 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. | ||
| 546 | |a English | ||
| 590 | |a School code: 0330 | ||
| 690 | |a Mathematics. | ||
| 710 | 2 | |a University of Chicago. |e degree granting institution. |0 http://id.loc.gov/authorities/names/n79058404 |1 http://viaf.org/viaf/143657677 | |
| 720 | 1 | |a Carlos Kenig |e degree supervisor. | |
| 720 | 1 | |a Panagiotis Souganidis |e degree supervisor. | |
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