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Paper   IPM / M / 12278
School of Mathematics
  Title:   On explicit representation and approximations of Dirichlet-to-Neumann semigroup
1.  H. Emamirad
2.  M. Sharifitabar
  Status:   Published
  Journal: Semigroup Forum
  Vol.:  86
  Year:  2013
  Pages:   192-201
  Supported by:  IPM
In his book (Functional Analysis, Wiley, New York, 2002), P. Lax constructs an explicit representation of the Dirichlet-to-Neumann semigroup, when the matrix of electrical conductivity is the identity matrix and the domain of the problem in question is the unit ball in Rn. We investigate some representations of Dirichlet-to- Neumann semigroup for a bounded domain. We show that such a nice explicit representation as in Lax book, is not possible for any domain except Euclidean balls. It is interesting that the treatment in dimension 2 is completely different than other dimensions. Finally, we present a natural and probably the simplest numerical scheme to calculate this semigroup in full generality by using Chernoff?s theorem.

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