PORTUGALIAE MATHEMATICA Vol. 53, No. 1, pp. 5372 (1996) 

An Inverse Problem for a General DoublyConnected Bounded Domain with Impedance Boundary ConditionsE.M.E. ZayedMathematics Department, Faculty of Science,Zagazig University, Zagazig  EGYPT Abstract: The spectral function $\theta(t)=\sum_{\nu=1}^{\infty}\exp(t\,\lambda_{\nu})$, where $\{\lambda_{\nu}\}_{\nu=1}^{\infty}$ are the eigenvalues of the negative Laplacian $\Delta=\sum_{i=1}^{2}(\frac{\partial}{\partial x^{i}})^{2}$ in the $(x^{1},x^{2})$plane, is studied for a general doublyconnected bounded domain $\Omega$ in $\R^{2}$ together with its smooth inner boundary $\partial\Omega_{1}$ and its smooth outer boundary $\partial\Omega_{2}$, where piecewise smooth impedance boundary conditions on the two parts $\Gamma_{1}$, $\Gamma_{2}$ of $\partial\Omega_{1}$ and on the two parts $\Gamma_{3}$, $\Gamma_{4}$ of $\partial\Omega_{2}$ are considered, such that $\partial\Omega_{1}=\Gamma_{1}\cup\Gamma_{2}$ and $\partial\Omega_{2}=\Gamma_{3}\cup\Gamma_{4}$. Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1996 Sociedade Portuguesa de Matemática
