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MSRI Summer Microprogram on Nonlinear Partial Differential Equations |
| July 23, 2007 to August 10, 2007 |
| Organized By: L. C. Evans (UC Berkeley, Chair), C. Gutierrez (Temple), C. Sogge (Johns Hopkins), D. Tataru (UC Berkeley) |
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| Return to Workshop Description |
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Lp bounds on eigenfunctions for Lipschitz metrics
Tuesday August 7, 2007
02:00PM - 03:00PM
Speakers:
Hart Smith
Abstract:
We consider the problem of establishing bounds on the Lp norm of eigenfunctions (or, more generally, spectrally localized
functions) on compact Riemannian manifolds without boundary.
Examples show that the bounds established by Sogge for smooth metrics can fail if the metric is not twice differentiable.
I will discuss recent joint work with Koch and Tataru in which we establish new (but likely not optimal) bounds in the case of Lipschitz metrics. A key ingredient is controlling the energy flow of solutions to a wave equation with Lipschitz metric.
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