| EPSRC Reference: |
GR/K00967/01 |
| Title: |
ELLIPTIC AND PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS |
| Principal Investigator: |
Davies, Professor EB |
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| Department: |
Mathematics |
| Organisation: |
Kings College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 1994 |
Ends: |
30 September 1997 |
Value (£): |
110,060
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Summary on Grant Application Form |
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Many related spectral problems concerning self-adjoint elliptic partial differential operators of order two or more are proposed for study. Spectral stability under L p perturbations of the highest order coefficients or under perturbations of very irregular boundaries is only now starting to be studied. These singular perturbation problems are much harder then those involving perturbations of lower order coefficients and their resolution will require new ideas. Much also remains to be done to control the rate of convergence of the homogenisation problem, that is the limit of vanishing period for operators with periodic coefficients. The long behaviour of the heat equation is not well controlled by present estimates, which are designed to understand the short time or high energy asymptotics. I hope to find connections between this and the description of zero energy resonances. Most of these problems have only been studied for second order operators but I hope to extend some of the results to higher order elliptic operators. ------------------------------------------------
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Key Findings |
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Potential use in non-academic contexts |
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| Description |
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Sectors submitted by the Researcher |
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