| EPSRC Reference: |
EP/J021490/1 |
| Title: |
Extremisers and near-extremisers for central inequalities in harmonic analysis, geometric analysis and PDE |
| Principal Investigator: |
Gutierez, Dr S |
| Other Investigators: |
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| Project Partners: |
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| Department: |
School of Mathematics |
| Organisation: |
University of Birmingham |
| Scheme: |
First Grant - Revised 2009 |
| Starts: |
15 February 2013 |
Ends: |
15 February 2014 |
Value (£): |
95,971
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| EPSRC Research Topic Classifications: |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Related Grants: |
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| Panel History: |
| Panel Date | Panel Name | Outcome |
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04 Jul 2012
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Mathematics Prioritisation Panel Meeting July 2012
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Announced
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Summary on Grant Application Form |
Isoperimetric inequalities are examples of sharp inequalities with intrinsic geometric content. The classical sharp inequality in two dimensions compares the area of an enclosed region in the plane with the length of its perimeter. Thanks to the sharpness, it is possible to deduce immediately that amongst all regions with a fixed perimeter length, the circle produces the maximum area. More generally, isoperimetric inequalities of this flavour can be used to identify maximising or minimising objects within a class, and they have applications in physical problems (for example, liquid droplet formation). Furthermore, these physical applications often demand that a "stable" version of the underlying sharp inequality is proved (to allow for the effect of external perturbative forces, for instance).
The main thrust of this broad project is to understand the sharpness and stability of some central inequalities which occur in harmonic analysis, geometric analysis and differential equations. These include the powerful Brascamp-Lieb inequality, which can be viewed as a generalised isoperimetric-type inequality and has fascinating and wide-ranging applications in the above fields and beyond. The project also encompasses sharp space-time inequalities for solutions of important differential equations, including the Schrodinger and wave equations.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.bham.ac.uk |