Sharp, Benjamin G. (2012) Compensation phenomena in geometric partial differential equations. PhD thesis, University of Warwick.

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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 or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Differential equations, Elliptic
Date:	25 June 2012
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Publication Status:	Unpublished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
URI:	http://wrap.warwick.ac.uk/id/eprint/50026

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