Details of Grant 

EPSRC Reference:	GR/T25002/01
Title:	Non-Linear Elliptic and Parabolic Equations in Differential Geometry
Principal Investigator:	Gibbon, Professor JD
Other Investigators:	Grigor'Yan, Professor A
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	Imperial College London
Scheme:	Standard Research (Pre-FEC)
Starts:	01 September 2004	Ends:	31 August 2006	Value (£):	74,083
EPSRC Research Topic Classifications:	Algebra & Geometry Mathematical Analysis
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
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Panel History:
Summary on Grant Application Form
1. Free-Boundary Problems in Geometric Flows and Related Topics: The aim is to study the short time regularity of solutions & interfaces as well as the all time regularity & the formation of singularities in free-boundary problems arising from the degeneracy of quasilinear & fully nonlinear geometric flows, such as the evolution Monge-Ampere equation, the Gauss curvature flow with flat sides or more general curvature flows. The understanding of such models of equations & free-boundary problems may have significant geometric & even topological applications. Related problems concerning the regularity of linear degenerate parabolic & elliptic equations are discussed.2. Regularity of Fully-Nonlinear Degenerate Elliptic Problems: regularity of solutions of degenerate Monge-Ampere equations & related elliptic freeboundary problems will be studied. It is motivated by the Weyl problem with non-negative Gaussian curvature.3. The Vanishing Behaviour of Solutions of the 2-dimensional Ricci Flow: This will deal with the type II blow up behaviour of maximal solutions of the 2-dimensional Ricci Flow correspond ing to complete Riemannian conformal metrics on a non-compact surface. Similar behaviours related to other fast-diffusions equations, such as the Yamabe flow in dimensions 3 and higher, will be studied.4. Strong intermittent turbulent behaviour of solutions of the Euler & Navier-Stokes equations is thought to be organized around the formation of singularities or near singularities (a speciality of JDG) the aim is to attempt to apply the methods of PD & R. Hamilton to these problems.
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Organisation Website:	http://www.imperial.ac.uk