Hadamard's variation of the Green kernels of heat equations and their traces I

Shin OZAWA

doi:10.2969/jmsj/03430455

Shin OZAWA

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JOURNAL FREE ACCESS

1982 Volume 34 Issue 3 Pages 455-473

DOI https://doi.org/10.2969/jmsj/03430455

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Published: 1982 Received: February 07, 1980 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) K. Aomoto, Formule variationnelle d'Hadamard et modèle euclidien des variétés différentiables plongées, J. Functional Analysis, 34 (1979), 493-523.
2) S. Bergmann and M. Schiffer, Kernel functions and elliptic differential equations in mathematical physics, Academic Press, New York, 1953.
3) D. Fujiwara and S. Ozawa, Hadamard's variational formula for the Green functions of some normal elliptic boundary value problems, Proc. Japan Acad., 54A (1978), 215-220.
4) D. Fujiwara, M. Tanikawa and S. Yukita, The spectrum of the Laplacian and boundary perturbation I, Proc. Japan Acad., 54A (1978), 87-91.
5) P. R. Garabedian, Partial differential equations, John Wiley and Sons, Inc., New York, 1964.
6) P. R. Garabedian and M. Schiffer, Convexity of domain functionals, J. Anal. Math., 2 (1952-53), 281-368.
7) J. Hadamard, Mémoire sur le problème d'analyse relatif à l'équilibre des plaques élastiques encastrées, CEuvres, C. N. R. S., tom. 2 (1968), 515-631.
8) S. Ozawa, Perturbation of domains and Green kernels of heat equations, Proc. Japan Acad., 54A (1978), 322-325.
9) S. Ozawa, Perturbation of domains and Green kernels of heat equations II, Proc. Japan Acad., 55A (1979), 172-175.
10) S. Ozawa, Deformation theory of domains and eigenvalues, Sugaku no Ayumi, 18 (1979), 135-164 (in Japanese).
11) J. Peetre, On Hadamard's variational formula, 1978, preprint.
12) M. Schiffer and D. C. Spencer, Functionals of finite Riemann surfaces, Princeton Univ. Press, 1954.
13) V. A. Solonnikov, On the boundary value problems for linear parabolic system of differential equations of general form, Trudy Mat. Inst. Steklov, 83 (1965), 1-184.

Right : [1] K. Aomoto, Formule variationnelle d'Hadamard et modèle euclidien des variétés différentiables plongées, J. Functional Analysis, 34 (1979), 493-523.
[2] S. Bergmann and M. Schiffer, Kernel functions and elliptic differential equations in mathematical physics, Academic Press, New York, 1953.
[3] D. Fujiwara and S. Ozawa, Hadamard's variational formula for the Green functions of some normal elliptic boundary value problems, Proc. Japan Acad., 54A (1978), 215-220.
[4] D. Fujiwara, M. Tanikawa and S. Yukita, The spectrum of the Laplacian and boundary perturbation I, Proc. Japan Acad., 54A (1978), 87-91.
[5] P. R. Garabedian, Partial differential equations, John Wiley and Sons, Inc., New York, 1964.
[6] P. R. Garabedian and M. Schiffer, Convexity of domain functionals, J. Anal. Math., 2 (1952-53), 281-368.
[7] J. Hadamard, Mémoire sur le problème d'analyse relatif à l'équilibre des plaques élastiques encastrées, CEuvres, C. N. R. S., tom. 2 (1968), 515-631.
[8] S. Ozawa, Perturbation of domains and Green kernels of heat equations, Proc. Japan Acad., 54A (1978), 322-325.
[9] S. Ozawa, Perturbation of domains and Green kernels of heat equations II, Proc. Japan Acad., 55A (1979), 172-175.
[10] S. Ozawa, Deformation theory of domains and eigenvalues, Sûgaku no Ayumi, 18 (1979), 135-164 (in Japanese).
[11] J. Peetre, On Hadamard's variational formula, 1978, preprint.
[12] M. Schiffer and D. C. Spencer, Functionals of finite Riemann surfaces, Princeton Univ. Press, 1954.
[13] V. A. Solonnikov, On the boundary value problems for linear parabolic system of differential equations of general form, Trudy Mat. Inst. Steklov, 83 (1965), 1-184.

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