An inverse problem for an inhomogeneous conformal Killing field equation

Author:
Ziqi Sun

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1583-1590

MSC (2000):
Primary 35R30, 53C21

DOI:
https://doi.org/10.1090/S0002-9939-02-06973-3

Published electronically:
December 16, 2002

MathSciNet review:
1949889

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Abstract: Let be a Riemannian metric defined on a bounded domain with boundary and let be a vector field on satisfying . We show that if is a gradient field of a solution to the equation on , then both inner products and are uniquely determined by the restriction of the tensor to the gradient field , where is the Lie derivative of the metric tensor under the vector field and . This work solves a problem related to an inverse boundary value problem for nonlinear elliptic equations.

**[B]**L. Bers, F. John, and M. Schechter,*Partial differential equations,*Interscience Publishers, New York, 1964. reprint MR**82c:35001****[H-Su]**D. Hervas and Z. Sun,*An inverse boundary value problem for quasilinear elliptic equations,*to appear in Comm. in PDE.**[He]**R. Hermann,*Differential geometry and the calculus of variations,*Academic Press, New York and London, 1968. MR**38:1635****[I 1]**V. Isakov,*On uniqueness in inverse problems for semilinear parabolic equations,*Arch. Rat. Mech.Anal.**124**(1993), 1-12.**[I 2]**V. Isakov,*Uniqueness of recovery of some systems of semilinear partial differential equations,*Inverse Problems**17**(2001) 607-618. MR**2002g:35213****[I-N]**V. Isakov and A. Nachman,*Global uniqueness for a two-dimensional semilinear elliptic inverse problem,*Trans. of AMS**347**(1995), 3375-3390. MR**95m:35202****[I-S]**V. Isakov and J. Sylvester,*Global uniqueness for a semilinear elliptic inverse problem,*Comm. Pure Appl. Math.**47**(1994), 1403-1410. MR**95h:35243****[Su]**Z. Sun,*On a quasilinear inverse boundary value problem,*Math. Z.**221**(1996), 293-305. MR**96m:35109****[Su-U]**Z. Sun and G. Uhlmann,*Inverse problems in quasilinear anisotropic media,*Amer. J. of Math.**119**(1997), 771-797. MR**98g:35216****[U]**G. Uhlmann,*Developments in inverse problems since Calderon's foundational paper,*Harmonic Analysis and Pde, University of Chicago Press, 1999. MR**2000m:35181****[Y]**K. Yano,*Integral formulas in Riemannian Geometry,*Marcel Dekker, Inc., New York, 1970. MR**44:2174**

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Additional Information

**Ziqi Sun**

Affiliation:
Department of Mathematics, Wichita State University, Wichita, Kansas 67260-0033

Email:
ziqi.sun@wichita.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06973-3

Received by editor(s):
January 8, 2002

Published electronically:
December 16, 2002

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2002
American Mathematical Society