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Estimates and regularity for some fully nonlinear PDEs in conformal geometry

Abstract:

In this thesis we obtain new estimates and regularity results for some fully nonlinear elliptic equations arising in conformal geometry.

Our first set of new results concern local pointwise second derivative estimates for elliptic solutions to the σk-Yamabe equation. In Chapter 2 we obtain such estimates for W2,p-strong solutions on Euclidean domains, addressing both the so-called positive and negative cases. We explore two methods for obtaining these estimates: an integ...

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Sub department:
Mathematical Institute
Oxford college:
Keble College
Role:
Author
ORCID:
0000-0002-6095-4055

Contributors

Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Sub department:
Mathematical Institute
Oxford college:
St Edmund Hall
Role:
Supervisor
ORCID:
0000-0002-1364-4433
More from this funder
Programme:
EPSRC Centre for Doctoral Training in Partial Differential Equations
Funding agency for:
Duncan, J
Grant:
EP/L015811/1
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford

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