Spectral Determination of Analytic Axi-symmetric Plane Domains
نویسنده
چکیده
Let D denote the class of bounded real analytic plane domains with the symmetry of an ellipse. We prove that if Ω1,Ω2 ∈ D and if the Dirichlet spectra coincide, Spec(Ω1) = Spec(Ω2), then Ω1 = Ω2 up to rigid motion.
منابع مشابه
Spectral Determination of Analytic Bi-axisymmetric Plane Domains
Let D denote the class of bounded real analytic plane domains with the symmetry of an ellipse. Under generic conditions, we prove that if Ω1,Ω2 ∈ D and if the Dirichlet spectra coincide, Spec(Ω1) = Spec(Ω2), then Ω1 = Ω2 up to rigid motion.
متن کاملAxi-Symmetric Deformation Due to Various Sources in Saturated Porous Media with Incompressible Fluid
The general solution of equations of saturated porous media with incompressible fluid for two dimensional axi-symmetric problem is obtained in the transformed domain. The Laplace and Hankel transforms have been used to investigate the problem. As an application of the approach concentrated source and source over circular region have been taken to show the utility of the approach. The transforme...
متن کاملStability of an inflated hyperelastic membrane tube with localized wall thinning
It is now well-known that when an infinitely long hyperelastic membrane tube free from any imperfections is inflated, a transcritical-type bifurcation may take place that corresponds to the sudden formation of a localized bulge. When the membrane tube is subjected to localized wall-thinning, the bifurcation curve would “unfold” into the turning-point type with the lower branch corresponding to ...
متن کاملO ct 2 00 4 INVERSE SPECTRAL PROBLEM FOR ANALYTIC DOMAINS II : Z 2 - SYMMETRIC DOMAINS STEVE
This paper develops and implements a new algorithm for calculating wave trace invariants of a bounded plane domain around a periodic billiard orbit. The algorithm is based on a new expression for the localized wave trace as a special multiple oscillatory integral over the boundary, and on a Feynman diagrammatic analysis of the stationary phase expansion of the oscillatory integral. The algorith...
متن کاملInverse Spectral Problem for Analytic Domains Ii: Z2- Symmetric Domains
This paper develops and implements a new algorithm for calculating wave trace invariants of a bounded plane domain around a periodic billiard orbit. The algorithm is based on a new expression for the localized wave trace as a special multiple oscillatory integral over the boundary, and on a Feynman diagrammatic analysis of the stationary phase expansion of the oscillatory integral. The algorith...
متن کامل