Notes on the mean value property for certain degenerate elliptic operators

Toshio HORIUCHI

doi:10.2969/jmsj/04610149

Toshio HORIUCHI

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ジャーナルフリー

1994 年 46 巻 1 号 p. 149-163

DOI https://doi.org/10.2969/jmsj/04610149

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Published: 1994 Received: 1992/03/17 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: 引用文献情報訂正内容: Wrong : 1) D. R. Adams, Weighted nonlinear potential theory, Trans. Amer. Math. Soc., 297 (1986), 73-94.
2) D. R. Adams and N. G. Meyers, Thinness and Wiener criteria for non-linear potentials, Indiana Univ. Math. J., 22 (1972), 139-158.
3) M. S. Baouendi and C. Goulaouic, Régularité et théorie spectrale pour une classe d'opérateurs elliptiques dégénérés, Arch. Rational Mech. Anal., 34 (1969), 361-379.
4) P. Bolley, J. Camus and G. Métivier, Estimations de Schauder et régularite Holderienne pour une classe de problèmes aux limites singulières, Comm. Partial Differential Equations, 11 (1986), 1135-1203.
5) L. Carleson, Selected problems on exceptional sets, Van Norstrand Co., Toronto-London-Melbourne, 1967.
6) G. Choquet, Theory of Capacities, Ann. Inst. Fourier, 5 (1955), 131-395.
7) J. L. Doob, Classical Potential Theory and its Probabilistic Counterpart, Springer, 1984.
8) C. Goulaouic and N. Shimakura, Régularité hölderienne de certains problèmes aux limites elliptiques dégénérés, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 10 (1983), 79-108.
9) C. R. Graham, The Dirichlet problem for the Bergman Laplacian II, Comm. Partial Differential Equations, 8 (1984), 563-641.
10) L. I. Hedberg and T. H. Wolff, Thin sets in nonlinear potential theory, Ann. Inst. Fourier, 33: 4 (1983), 161-187.
11) T. Horiuchi, Existence and uniqueness of classical solutions for certain degenerated elliptic equations of second order, J. Math. Kyoto Univ., 24 (1984), 557-576.
12) N. S. Landkof, Foundations of Modern Potential Theory, Springer, 1972.
13) V. G. Maz'ja and V. P. Havin, A nonlinear analogue of the Newton potential and metric properties of the (p, l)-capacity, Soviet Math. Dokl., 11 (1970), 1294-1298.
14) V. G. Maz'ja and V. P. Havin, Nonlinear potential theory, Russian Math. Surveys, 27 (1972), 71-148.
15) N. G. Meyers, A theory of capacities for potentials of functions in Lebesgue class, Math. Scand., 26 (1970), 255-292.
16) E. W. Stredulinsky, Weighted inequalities and degenerate elliptic partial differential equations, Lecture Notes in Math., 1074, Springer, 1984.

Right : [1] D. R. Adams, Weighted nonlinear potential theory, Trans. Amer. Math. Soc., 297 (1986), 73-94.
[2] D. R. Adams and N. G. Meyers, Thinness and Wiener criteria for non-linear potentials, Indiana Univ. Math. J., 22 (1972), 139-158.
[3] M. S. Baouendi and C. Goulaouic, Régularité et théorie spectrale pour une classe d'opérateurs elliptiques dégénérés, Arch. Rational Mech. Anal., 34 (1969), 361-379.
[4] P. Bolley, J. Camus and G. Métivier, Estimations de Schauder et régularite Hölderienne pour une classe de problèmes aux limites singulières, Comm. Partial Differential Equations, 11 (1986), 1135-1203.
[5] L. Carleson, Selected problems on exceptional sets, Van Norstrand Co., Toronto-London-Melbourne, 1967.
[6] G. Choquet, Theory of Capacities, Ann. Inst. Fourier, 5 (1955), 131-395.
[7] J. L. Doob, Classical Potential Theory and its Probabilistic Counterpart, Springer, 1984.
[8] C. Goulaouic and N. Shimakura, Régularité hölderienne de certains problèmes aux limites elliptiques dégénérés, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 10 (1983), 79-108.
[9] C. R. Graham, The Dirichlet problem for the Bergman Laplacian II, Comm. Partial Differential Equations, 8 (1984), 563-641.
[10] L. I. Hedberg and T. H. Wolff, Thin sets in nonlinear potential theory, Ann. Inst. Fourier, 33: 4 (1983), 161-187.
[11] T. Horiuchi, Existence and uniqueness of classical solutions for certain degenerated elliptic equations of second order, J. Math. Kyoto Univ., 24 (1984), 557-576.
[12] N. S. Landkof, Foundations of Modern Potential Theory, Springer, 1972.
[13] V. G. Maz'ja and V. P. Havin, A nonlinear analogue of the Newton potential and metric properties of the (p, l)-capacity, Soviet Math. Dokl., 11 (1970), 1294-1298.
[14] V. G. Maz'ja and V. P. Havin, Nonlinear potential theory, Russian Math. Surveys, 27 (1972), 71-148.
[15] N. G. Meyers, A theory of capacities for potentials of functions in Lebesgue class, Math. Scand., 26 (1970), 255-292.
[16] E. W. Stredulinsky, Weighted inequalities and degenerate elliptic partial differential equations, Lecture Notes in Math., 1074, Springer, 1984.

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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