Convex shape optimization for the least biharmonic Steklov eigenvalue
Pedro Ricardo Simão Antunes, Filippo Gazzola (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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The least Steklov eigenvalue for the biharmonic operator in bounded domains gives a bound for the positivity preserving property for the hinged plate problem, appears as a norm of a suitable trace operator, and gives the optimal constant to estimate the -norm of harmonic functions. These applications suggest to address the problem of minimizing in suitable classes of domains. We survey the existing results and conjectures about this topic;...