Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



An inverse problem for a general convex domain with impedance boundary conditions

Authors: E. M. E. Zayed and A. I. Younis
Journal: Quart. Appl. Math. 48 (1990), 181-188
MSC: Primary 35R30; Secondary 35C99, 35P05, 58G25
DOI: https://doi.org/10.1090/qam/1040241
MathSciNet review: MR1040241
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Abstract: The spectral function $ \theta \left( t \right) = \sum\nolimits_{n = 1}^\infty {\exp \left( { - t{\lambda _n}} \right)} $, where $ \left\{ {{\lambda _n}} \right\}_{n = 1}^\infty $ are the eigenvalues of the Laplace operator $ \Delta = \sum\nolimits_{i = 1}^2 {{{\left( {\partial /\partial {x^i}} \right)}^2}} $ in the $ {x^1}{x^2}$-plane, is studied for a general convex domain $ \Omega \subseteq {R^2}$ with a smooth boundary $ \partial \Omega $ together with a finite number of piecewise smooth impedance boundary conditions on the parts $ {\Gamma _{1,...,}}{\Gamma _m}$ of $ \partial \Omega $ such that $ \partial \Omega = U_{j = 1}^m{\Gamma _j}$.

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DOI: https://doi.org/10.1090/qam/1040241
Article copyright: © Copyright 1990 American Mathematical Society

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