Optimal lower bound of the resonance widths for the Helmholtz Resonator

Abstract

Under a geometric assumption on the region near the end of its neck, we prove an optimal exponential lower bound on the widths of resonances for a general two-dimensional Helmholtz resonator. An extension of the result to the n-dimensional case, n smaller than 12, is also obtained.

arXiv comment25 pages, 2 figures