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• W2520422574 abstract "Abstract We consider minimizers of urn:x-wiley:00103640:media:cpa21810:cpa21810-math-0001 where F is a function nondecreasing in each parameter, and λ k (Ω) is the k th Dirichlet eigenvalue of ω. This includes, in particular, functions F that depend on just some of the first N eigenvalues, such as the often‐studied F = λ N . The existence of a minimizer, which is also a bounded set of finite perimeter, was shown recently. Here we show that the reduced boundary of the minimizers Ω is made up of smooth graphs and examine the difficulties in classifying the singular points. Our approach is based on an approximation (“vanishing viscosity”) argument, which—counterintuitively—allows us to recover an Euler‐Lagrange equation for the minimizers that is not otherwise available. © 2019 Wiley Periodicals, Inc." @default.
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• W2520422574 date "2019-04-08" @default.
• W2520422574 modified "2023-09-29" @default.
• W2520422574 title "Regularity for Shape Optimizers: The Degenerate Case" @default.
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• W2520422574 doi "https://doi.org/10.1002/cpa.21810" @default.
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