The Library
Compensation phenomena in geometric partial differential equations
Tools
Sharp, Benjamin G. (2012) Compensation phenomena in geometric partial differential equations. PhD thesis, University of Warwick.
|
Text
WRAP_THESIS_Sharp_2012.pdf - Submitted Version Download (1248Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b2582742~S1
Abstract
In this thesis we present optimal and improved estimates for systems of critical
elliptic PDE which arise as generalisations of natural geometric problems. We provide
optimal regularity and compactness results for ‘Rivière’s equation’ for two dimensional
domains via a new decay estimate, andwe exhibit examples to showthat the results are
sharp. These results are presented in chapters 4 and 5. Such estimates generalise and
improve known results in the classical setting.
In chapter 6 we improve the known regularity for the higher dimensional theory introduced
by Rivière-Struwe leading to better estimates for solutions in this case. Such
estimates in particular lead to an easy proof for the regularity for stationary harmonic
maps.
We also present (in chapter 7) sharp results for a complex system of PDE, a consequence
of which is a short proof of the full regularity for weakly harmonic maps from
a Riemann surface into a closed Riemannian manifold.
Item Type: | Thesis (PhD) | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Differential equations, Elliptic | ||||
Official Date: | 25 June 2012 | ||||
Dates: |
|
||||
Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Topping, Peter, 1971- | ||||
Sponsors: | Leverhulme Trust (LT) | ||||
Extent: | vi, 113 leaves | ||||
Language: | eng |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year