Roman Chapko1, B. Tomas Johansson2
CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.2, pp. 105-128, 2012, DOI:10.3970/cmes.2012.085.105
Abstract We consider a Cauchy problem for the Laplace equation in a 3-dimen -sional semi-infinite domain that contains a bounded inclusion. The canonical situation is the upper half-space in I\tmspace -.1667em R3 containing a bounded smooth domain. The function value of the solution is specified throughout the plane bounding the upper half-space, and the normal derivative is given only on a finite portion of this plane. The aim is to reconstruct the solution on the surface of the bounded inclusion. This is a generalisation of the situation in Chapko and Johansson (2008) to three-dimensions and with Cauchy data only partially given.… More >
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