Regularity of Optimal Shapes for the Dirichlet ’ S Energy with Volume Constraint ∗

  title={Regularity of Optimal Shapes for the Dirichlet ’ S Energy with Volume Constraint ∗},
  author={Tanguy Briancon}
  • Tanguy Briancon
In this paper, we prove some regularity results for the boundary of an open subset of R which minimizes the Dirichlet’s energy among all open subsets with prescribed volume. In particular we show that, when the volume constraint is “saturated”, the reduced boundary of the optimal shape (and even the whole boundary in dimension 2) is regular if the state function is nonnegative. Mathematics Subject Classification. 35R35, 49N60, 49Q10. Received 25 February 2003. Revised 4 August 2003… CONTINUE READING

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