Optimal lower bound of the resonance widths for a Helmholtz tube-shaped resonator (Q421854)

Summary: The study of the resonances of the Helmholtz resonator has been broadly described in previous works (see [\textit{R. A. Adams}, Sobolev spaces. New York-San Francisco-London: Academic Press (1975; Zbl 0314.46030)] and references therein). Here, for a simple 2-dimensional resonator in the shape of a tube, we analyze the transition zone where oscillations start to appear. Following a careful analysis, we obtain an optimal lower bound of the width of the resonances.