On the Spectral Gap for Convex Domains
نویسنده
چکیده
Let D be a convex planar domain, symmetric about both the xand y-axes, which is strictly contained in (−a, a) × (−b, b) = Γ. It is proved that, unless D is a certain kind of rectangle, the difference (gap) between the first two eigenvalues of the Dirichlet Laplacian in D is strictly larger than the gap for Γ. We show how to give explicit lower bounds for the difference of the gaps.
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