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- W4307183727 abstract "We consider minimizers of [ F(lambda_1(Omega),ldots,lambda_N(Omega)) + |Omega|, ] where $F$ is a function nondecreasing in each parameter, and $lambda_k(Omega)$ is the $k$-th Dirichlet eigenvalue of $Omega$. This includes, in particular, functions $F$ which depend on just some of the first $N$ eigenvalues, such as the often studied $F=lambda_N$. 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 $Omega$ 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 which is not otherwise available." @default.
- W4307183727 created "2022-10-29" @default.
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- W4307183727 date "2017-10-01" @default.
- W4307183727 modified "2023-09-29" @default.
- W4307183727 title "Regularity for Shape Optimizers: The Degenerate Case" @default.
- W4307183727 doi "https://doi.org/10.48550/arxiv.1710.00451" @default.
- W4307183727 hasPublicationYear "2017" @default.
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