Energy Measurements and Equivalence of Boundary Data for Inverse Problems on Non-Compact Manifolds
The goal of this paper is to consider inverse problems with different types of boundary data given as boundary forms. In particular, the boundary measurements considered in this paper are related to the measurements of energy needed to force the boundary value of a physical field to a given one.
KeywordsInverse Problem Riemannian Manifold Gauge Transformation Gaussian Beam Boundary Data
Unable to display preview. Download preview PDF.
- [C1]Calderón, A.P. On an inverse boundary value problem. Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro, 1980), pp. 65–73, Soc. Brasil. Mat., Rio de Janeiro, 1980.Google Scholar
- [KKL]Katchalov, A., Kurylev, Y., Lassas, M. Inverse boundary spectral problems, Chapman&Hall/CRC, 2001, pp. 290.Google Scholar
- [KKLM]Katchalov, A., Kurylev, Y., Lassas, M., Mandache N. Equivalence of time- domain inverse problems and boundary spectral problems. Submitted to Inv. Prob I. Google Scholar
- [KaL]Katchalov A., Lassas M. Gaussian beams and inverse boundary spectral problems, in: New Geom. and Anal. Meth. in Inv. Probl. (Eds. Y. Kurylev and E. Somersalo), Springer Lect. Notes, to appear.Google Scholar
- [KaKuLa]Katsuda A., Kurylev Y., Lassas M. Stability on inverse boundary spectral problem, in: New Geom. and Anal. Meth. in Inv. Probl. (Eds. Y. Kurylev and E. Somersalo), Springer Lect. Notes, to appear.Google Scholar
- [KaKuLT]Katsuda A, Kurylev Y, Lassas M. and Taylor M. Geometric convergence for manifolds with boundary. In preparation.Google Scholar
- [Ko]Koosis P. Introduction to Hp Spaces, Cambr. Univ. Press, 1998, pp. 287.Google Scholar
- [K2]Kurylev, Y. Multidimensional Gel’fand inverse problem and boundary dis tance map. Inv. Probl. related Geom., Mito (1997), 1–15.Google Scholar
- [KL1]Kurylev, Y., Lassas, M. Hyperbolic inverse problem with data on a part of the boundary. Differential Equations and Mathematical Physics (Birmingham, AL, 1999), 259–272, AMS/IP Stud. Adv. Math., 16, Amer. Math. Soc., Providence, 2000.Google Scholar
- [KL2]Kurylev, Y., Lassas, M. Hyperbolic inverse problem and unique continuation of Cauchy data of solutions along the boundary, Proc. Roy. Soc. Edinburgh, Ser. A, to appear.Google Scholar
- [RS]Reed M., Simon B. Methods of Modern Mathematical Physics, v. l, Acad. Press, New York-London, 1972.Google Scholar
- [Shi]Shubin M. Spectral theory of elliptic operators on non-compact manifolds. Asterisque 207 (1992), 37–108.Google Scholar