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Inverse problem in electrostatics with free boundary

Activity: Talk or presentationConference presentation

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Jukka-Pekka Humaloja - Speaker

Consider an electrical potential u satisfying Laplace's equation on a plane region with mixed boundary conditions. We are interesting in solving a parametrization for one of the domain's boundary curves based on Cauchy data on the opposite boundary The problem is solved with a variation of alternating field technique on inverted plane. Let v be the harmonic conjugate of u. Then the function u(x, y) + iv(x, y) is analytic and it has an inverse x(u, v) + iy(u, v). The functions x and y satisfy Laplace's equation on a rectangle, and the unknown boundary curve maps to unknown boundary conditions in the rectangle. The unknown boundary conditions are solved using the alternating-field technique.
10 Jan 2014

Event (Conference)

TitleFinEst Math 2014, Finnish-Estonian Mathematical Colloquium 2014, 9-10 January, 2014
Period1/01/14 → …

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