“School of Mathematics”
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| Paper IPM / M / 12278 |
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| Abstract: | |||||
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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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