On the coercivity of the hyperbolic single layer potential
A talk in the BI.discrete Workshop series by
Martin Costabel from Rennes
| Abstract: | The scattering of acoustic waves by an open surface ("screen") can be described by a single layer representation, giving rise to a first kind
space-time boundary integral equation on the screen. This integral equation
has been used for a long time for numerical approximations, and an important
argument in the analysis of such numerical methods is the coercivity of the
integral operator. This means that one wishes to estimate the quadratic form
associated with the operator from above and from below. In the case of a flat
screen, the operator is a Fourier multiplier, and one has to estimate its
symbol. Known sharp estimates use two different norms for the two estimates,
but one can show that with a quadratic form involving the Hilbert
transformation in time, one can get coercivity with only one norm, which is a
somewhat unusual Sobolev norm. Attendance is only possible after registration with the organizers and with 3G-certificate. Within the CRC this talk is associated to the project(s): A7, B7 |