| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | June 7, 2006 |
| Latest Amendment Date: | May 11, 2010 |
| Award Number: | 0601162 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Bruce P. Palka
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | July 1, 2006 |
| End Date: | June 30, 2011 (Estimated) |
| Total Intended Award Amount: | $0.00 |
| Total Awarded Amount to Date: | $161,999.00 |
| Funds Obligated to Date: |
FY 2008 = $40,000.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
500 S LIMESTONE LEXINGTON KY US 40526-0001 (859)257-9420 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
500 S LIMESTONE LEXINGTON KY US 40526-0001 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | ANALYSIS PROGRAM |
| Primary Program Source: |
01000809DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
L-infinity variational problems are problems where one seeks to find the maximum (or minimum) of a functional that is an expression involving the pointwise behavior of a function and its gradient. The study of such problems has become very active recently and this project will support the study of a number of important open questions in the area. A particular interest is the relationship between minimizers of the variational problems and solutions of the corresponding Aronsson equation. Other questions include the uniqueness and regularity of solutions of the Aronsson equations and the characterization of the principal eigenvalue of the infinity-Laplacian operator.
These variational problems are not only interesting mathematically but arise in a number of different areas of applications. These include the determination of optimal radiation treatments in chemotherapy, in image analysis and reconstruction and in determining winning strategies in certain types of games. The results obtained under this research will help describe the mathematical models of these applications. This is a collaborative award with Dr Yifeng Yu of the University of Texas at Austin.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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