Corpus ID: 231918437

The Dirichlet-to-Neumann map, the boundary Laplacian, and H\"ormander's rediscovered manuscript

  title={The Dirichlet-to-Neumann map, the boundary Laplacian, and H\"ormander's rediscovered manuscript},
  author={Alexandre Girouard and Mikhail A. Karpukhin and Michael Levitin and Iosif Polterovich},
How close is the Dirichlet-to-Neumann (DtN) map to the square root of the corresponding boundary Laplacian? This question has been actively investigated in recent years. Somewhat surprisingly, a lot of techniques involved can be traced back to a newly rediscovered manuscript of Hörmander from the 1950s. We present Hörmander’s approach and its applications, with an emphasis on eigenvalue estimates and spectral asymptotics. In particular, we obtain results for the DtN maps on non-smooth… Expand

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