On the Dirichlet problem for quasi-linear elliptic differential equations of the second order

Kiyoshi AKÔ

doi:10.2969/jmsj/01310045

Kiyoshi AKÔ

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ジャーナルフリー

1961 年 13 巻 1 号 p. 45-62

DOI https://doi.org/10.2969/jmsj/01310045

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Published: 1961 Received: 1960/04/21 Available on J-STAGE: 2006/08/29 Accepted: - Advance online publication: - Revised: -
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訂正日: 2006/08/29 訂正理由: - 訂正箇所: 著者情報訂正内容: Wrong : Kiyoshi AKO¹⁾
Right : Kiyoshi AKÔ¹⁾

訂正日: 2006/08/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Right : [1] S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, Part I, Comm. Pure Appl. Math., 12 (1959), 623-727.
[2] L. Bers and L. Nirenberg, On linear and non-linear elliptic boundary value problems in the plane, Convegno Internazionale sulle Equazioni Derivate Parziali, Trieste, (1954), 141-167.
[3] H. O. Cordes, Über die erste Randwertaufgabe bei quasi-linearer Differentialgleichungen zweiter Ordnung in mehr als zwei Variablen, Math. Ann., 131 (1956), 278-312.
[4] N. Dunford and J. T. Schwartz, Linear Analysis, Part I, Interscience, New York, 1958.
[5] I. Hirai and K. Akô, On generalized Peano's theorem concerning the Dirichlet problem of semi-linear elliptic differential equations of the second order, to appear.
[6] E. Hopf, Elementare Bemerkungen zweiter Ordnung vom elliptischen Typus, Sitzungsberichte Preuss. Akad. Wiss. Berlin, (1927), 145-152.
[7] M. Hukuhara, Jô Bibun Hôteishiki (Ordinary Differential Equations), 1950 (Iwanami, Tokyo, in Japanese).
[8] E. Kamke, Differentialgleichungen, Lösungsmethoden und Lösungen, Akademie Verlag, Leibzig, 1943.
[9] C. Miranda, Equazioni alle Derivate Parziali di Tipo Ellitico, Springer, Berlin, 1955.
[10] M. Nagumo, On principally linear elliptic differential equations of the second order, Osaka Math. J., 6, (1954), 207-229.
[11] L. Nirenberg, On nonlinear elliptic differential equations and Hölder continuity, Comm. Pure Appl. Math., 6 (1953), 103-156.
[12] L. Nirenberg, Estimates and Existence of solutions of elliptic equations, Comm. Pure Appl. Math., 9 (1956), 509-530.
[13] J. Schauder, Über lineare elliptische Differentialgleichungen zweiter Ordnung, Math. Z., 38 (1934), 257-282.
[14] J. Schauder, Numerische Abschätzungen in elliptischen linearen Differentialgleichungen, Studia Math., 5 (1934), 35-42.

訂正日: 2006/08/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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