Semi-linear second-order elliptic equations in L1

Haïm BREZIS; Walter A. STRAUSS

doi:10.2969/jmsj/02540565

Semi-linear second-order elliptic equations in L¹

Haïm BREZIS, Walter A. STRAUSS

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ジャーナルフリー

1973 年 25 巻 4 号 p. 565-590

DOI https://doi.org/10.2969/jmsj/02540565

詳細

Published: 1973 Received: 1972/09/09 Available on J-STAGE: 2006/09/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/29 訂正理由: - 訂正箇所: 論文タイトル訂正内容: Wrong : Semi-linear second-order elliptic equations in L¹
Right : Semi-linear second-order elliptic equations in L¹

訂正日: 2006/09/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math., 12 (1959), 623-727.
2) H. Brezis, Propriétés régularisantes de certains semi-groupes non linéaires, Israel J. Math., 9 (1971), 513-534.
3) F. E. Browder, Remarks on nonlinear interpolation in Banach spaces, J. Func. Anal., 4 (1969), 390-403.
4) F. E. Browder, Existence theory for boundary value problems for quasilinear elliptic systems with strongly nonlinear lower order terms, Berkeley conference on partial differential equations, August, 1971.
5) M. G. Crandall, Semigroups of nonlinear transformations in Banach spaces, Contributions to Nonlinear Functional Analysis, Academic Press, 1971.
6) M. G. Crandall and A. Pazy, Semi-groups of nonlinear contractions and dissipative sets, J. Func. Anal., 3 (1969), 376-418.
7) G. DaPrato, Somme d'applications non linéaires, Symposia Mathematica VII, 1st. Naz. di Alta Mat., Academic Press, 1971, p. 262.
8) G. H. Hardy, J. Littlewood and G. Polya, Inequalities, Cambridge University Press, 1952, Exercise 249, p. 170.
9) P. Hartman and G. Stampacchia, On some nonlinear elliptic differential-functional equations, Acta Math., 115 (1966), 271-310.
10) Y. Konishi, Une remarque sur la perturbation d'opérateurs m-accrétifs dans un espace de Banach, Proc. Japan Acad., 48 (1972), 157-160.
11) M. A. Krasnoselskii and Ya. B. Rutickii, Convex Functions and Orlicz Spaces, Moscow, 1958.
12) J. Leray and J. L. Lions, Quelques résultats de Visik sur les problèmes elliptiques nonlinéaires par les méthodes de Minty-Browder, Bull. Soc. Math. France, 93 (1965), 97-107.
13) J. L. Lions, Some remarks on variational inequalities, Proc. Int. Conf. Functional Analysis (Tokyo, 1969), Univ. of Tokyo Press, 1970, 269-282.
14) J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math., 14 (1961), 577-591.
15) R. C. O'Neil, Fractional Integration and Orlicz Spaces, Thesis, Univ. of Chicago, 1960, p. 39.
16) J. Peetre, Interpolation of Lipschitz operators and metric spaces, Mathematica (Cluj), 12 (35), 2 (1970), 325-334.
17) G. Stampacchia, On some regular multiple integral problems in the calculus of variations, Comm. Pure Appl. Math., 16 (1963), 383-421.
18) G. Stampacchia, Some limit cases of L^p-estimates for solutions of second order elliptic equations, Comm. Pure Appl. Math., 16 (1963), 505-510.
19) E. Stein, Note on the class L log L, Studia Math., 32 (1969), 305-310.
20) W. A. Strauss, On weak solutions of semi-linear hyperbolic equations, Anais Acad. Brasil. Ciências, 42 (1970), 645-651.

Right : [1] S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math., 12 (1959), 623-727.
[2] H. Brezis, Propriétés régularisantes de certains semi-groupes non linéaires, Israel J. Math., 9 (1971), 513-534.
[3] F. E. Browder, Remarks on nonlinear interpolation in Banach spaces, J. Func. Anal., 4 (1969), 390-403.
[4] F. E. Browder, Existence theory for boundary value problems for quasilinear elliptic systems with strongly nonlinear lower order terms, Berkeley conference on partial differential equations, August, 1971.
[5] M. G. Crandall, Semigroups of nonlinear transformations in Banach spaces, Contributions to Nonlinear Functional Analysis, Academic Press, 1971.
[6] M. G. Crandall and A. Pazy, Semi-groups of nonlinear contractions and dissipative sets, J. Func. Anal., 3 (1969), 376-418.
[7] G. DaPrato, Somme d'applications non linéaires, Symposia Mathematica VII, Ist. Naz. di Alta Mat., Academic Press, 1971, p. 262.
[8] G. H. Hardy, J. Littlewood and G. Polya, Inequalities, Cambridge University Press, 1952, Exercise 249, p. 170.
[9] P. Hartman and G. Stampacchia, On some nonlinear elliptic differential-functional equations, Acta Math., 115 (1966), 271-310.
[10] Y. Konishi, Une remarque sur la perturbation d'opérateurs m-accrétifs dans un espace de Banach, Proc. Japan Acad., 48 (1972), 157-160.
[11] M. A. Krasnoselskii and Ya. B. Rutickii, Convex Functions and Orlicz Spaces, Moscow, 1958.
[12] J. Leray and J. L. Lions, Quelques résultats de Visik sur les problèmes elliptiques nonlinéaires par les méthodes de Minty-Browder, Bull. Soc. Math. France, 93 (1965), 97-107.
[13] J. L. Lions, Some remarks on variational inequalities, Proc. Int. Conf. Functional Analysis (Tokyo, 1969), Univ. of Tokyo Press, 1970, 269-282.
[14] J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math., 14 (1961), 577-591.
[15] R. C. O'Neil, Fractional Integration and Orlicz Spaces, Thesis, Univ. of Chicago, 1960, p. 39.
[16] J. Peetre, Interpolation of Lipschitz operators and metric spaces, Mathematica (Cluj), 12 (35), 2 (1970), 325-334.
[17] G. Stampacchia, On some regular multiple integral problems in the calculus of variations, Comm. Pure Appl. Math., 16 (1963), 383-421.
[18] G. Stampacchia, Some limit cases of L^p-estimates for solutions of second order elliptic equations, Comm. Pure Appl. Math., 16 (1963), 505-510.
[19] E. Stein, Note on the class L log L, Studia Math., 32 (1969), 305-310.
[20] W. A. Strauss, On weak solutions of semi-linear hyperbolic equations, Anais Acad. Brasil. Ciências, 42 (1970), 645-651.

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