New bounds on Dirichlet eigenfunction efficiency for convex domains show the Payne-Stakgold bound is not optimal and a maximizer exists among planar convex sets.
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Maximization of the efficiency of the first Dirichlet eigenfunction and improved eigenvalue inequalities
New bounds on Dirichlet eigenfunction efficiency for convex domains show the Payne-Stakgold bound is not optimal and a maximizer exists among planar convex sets.