Old and new bounds on solutions of the Helmholtz equation proved by integrating by parts
A classic technique in PDE theory is that of multiplying by a carefully-chosen test function and integrating by parts. This method was famously used to prove bounds on the Helmholtz equation in the 1960s and 1970s by Cathleen Morawetz. Much-more sophisticated methods now exist for proving bounds on the Helmholtz equation, but (perhaps surprisingly) the multiplier method can still be used to prove new results. In this talk I will review the classic multiplier method, and then discuss a recent application of it to Helmholtz problems in the paper "Scattering by finely-layered obstacles: frequency-explicit bounds and homogenization" https://arxiv.org/abs/2109.11267 , co-authored with Th\'eophile Chaumont-Frelet (INRIA, Nice).
Place: Hybrid, Math, 402 and
Password: “arizona” (all lower case)