Solutions of the Dirichlet problem on a cone with continuous data

Hidenobu YOSHIDA; Ikuko MIYAMOTO

doi:10.2969/jmsj/05010071

Hidenobu YOSHIDA, Ikuko MIYAMOTO

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ジャーナルフリー

1998 年 50 巻 1 号 p. 71-93

DOI https://doi.org/10.2969/jmsj/05010071

詳細

Published: 1998 Received: 1995/08/10 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル訂正内容: Wrong : Dedicated to Professor Yasuo Okuyama on his 60th birthday

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) D. H. Armitage, Representations of harmonic functions in half-spaces, Proc. London Math. Soc. (3) 38 (1979), 53-71.
2) V. S. Azarin, Generalization of a theorem of Hayman on subharmonic functions in an m-dimensional cone, Mat. Sb. 66 (108) (1965), 248-264; Amer. Math. Soc. Translation (2) 80 (1969), 119-138.
3) M. Brelot, Elements de la théorie classique du potentiel, Centre de Documentation Universitaire, Paris, 1965
4) S. Y. Cheng and P. Li, Heat kernel estimates and lower bound of eigenvalues, Comment. Math. Helvetici 56 (1981), 327-338.
5) R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 1 Interscience Publishers, New York, 1953.
6) B. E. J. Dahlberg, Estimates of harmonic measure, Arch. Rational Mech. Anal. 65 (1977), 257-288.
7) M. Essén and J. L. Lewis, The generalized Ahlfors-Heins theorems in certain d-dimensional cones, Math. Scand. 33 (1973), 111-129.
8) M. Finkelstein and S. Scheinberg, Kernels for solving problems of Dirichlet type in a half-plane, Advances in Math. 18 (1975), 108-113.
9) S. J. Gardiner, The Dirichlet and Neumann problems for harmonic functions in half-spaces, J. London Math. Soc. (2) 24 (1981), 502-512.
10) D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Springer Verlag, Berlin, 1977.
11) W. K. Hayman and P. B. Kennedy, Subharmonic Functions, Vol. 1 Academic Press, London, 1976.
12) S. Helgason, Differential geometry and symmetric spaces, Academic Press, London, 1962.
13) L. L. Helms, Introduction to Potential Theory, Wiley-Interscience, New York, 1969.
14) S. Minakshisundaram and A. Pleijel, Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds, Canad. J. Math. 1 (1949), 242-256.
15) R. Nevanlinna, Über eine Erweiterung des Poissonschen Integrals, Ann. Acad. Sci. Fenn. Ser. A 24 (4) (1925), 1-15.
16) D. Siegel, The Dirichlet problem in a half-spaces and a new Phragmén-Lindelöf principle, Maximum Principles and Eigenvalue Problems in Partial Differential Equations, e.d. P. W. Schaefer, Pitman, New York, 1988.
17) H. Yoshida, Nevanlinna norm of a subharmonic function on a cone or on a cylinder, Proc. London Math. Soc. (3) 54 (1987), 267-299.
18) H. Yoshida, Harmonic majorization of a subharmonic function on a cone or on a cylinder, Pacific J. Math. 148 (1991), 369-395.
19) H. Yoshida, A type of uniqueness for the Dirichlet problem on a half-space with continuous data, Pacific J. Math. 172 (1996), 591-609.
20) H. Yoshida and I. Miyamoto, Harmonic functions in a cone which vanish on the boundary, Math. Nachr. (to appear).

Right : [1] D. H. Armitage, Representations of harmonic functions in half-spaces, Proc. London Math. Soc. (3) 38 (1979), 53-71.
[2] V. S. Azarin, Generalization of a theorem of Hayman on subharmonic functions in an m-dimensional cone, Mat. Sb. 66 (108) (1965), 248-264; Amer. Math. Soc. Translation (2) 80 (1969), 119-138.
[3] M. Brelot, Elements de la théorie classique du potentiel, Centre de Documentation Universitaire, Paris, 1965
[4] S. Y. Cheng and P. Li, Heat kernel estimates and lower bound of eigenvalues, Comment. Math. Helvetici 56 (1981), 327-338.
[5] R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 1 Interscience Publishers, New York, 1953.
[6] B. E. J. Dahlberg, Estimates of harmonic measure, Arch. Rational Mech. Anal. 65 (1977), 257-288.
[7] M. Essén and J. L. Lewis, The generalized Ahlfors-Heins theorems in certain d-dimensional cones, Math. Scand. 33 (1973), 111-129.
[8] M. Finkelstein and S. Scheinberg, Kernels for solving problems of Dirichlet type in a half-plane, Advances in Math. 18 (1975), 108-113.
[9] S. J. Gardiner, The Dirichlet and Neumann problems for harmonic functions in half-spaces, J. London Math. Soc. (2) 24 (1981), 502-512.
[10] D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Springer Verlag, Berlin, 1977.
[11] W. K. Hayman and P. B. Kennedy, Subharmonic Functions, Vol. 1 Academic Press, London, 1976.
[12] S. Helgason, Differential geometry and symmetric spaces, Academic Press, London, 1962.
[13] L. L. Helms, Introduction to Potential Theory, Wiley-Interscience, New York, 1969.
[14] S. Minakshisundaram and A. Pleijel, Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds, Canad. J. Math. 1 (1949), 242-256.
[15] R. Nevanlinna, Über eine Erweiterung des Poissonschen Integrals, Ann. Acad. Sci. Fenn. Ser. A 24 (4) (1925), 1-15.
[16] D. Siegel, The Dirichlet problem in a half-spaces and a new Phragmén-Lindelöf principle, Maximum Principles and Eigenvalue Problems in Partial Differential Equations, e. d. P. W. Schaefer, Pitman, New York, 1988.
[17] H. Yoshida, Nevanlinna norm of a subharmonic function on a cone or on a cylinder, Proc. London Math. Soc. (3) 54 (1987), 267-299.
[18] H. Yoshida, Harmonic majorization of a subharmonic function on a cone or on a cylinder, Pacific J. Math. 148 (1991), 369-395.
[19] H. Yoshida, A type of uniqueness for the Dirichlet problem on a half-space with continuous data, Pacific J. Math. 172 (1996), 591-609.
[20] H. Yoshida and I. Miyamoto, Harmonic functions in a cone which vanish on the boundary, Math. Nachr. (to appear).

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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