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

Author information

JOURNAL FREE ACCESS

1973 Volume 25 Issue 4 Pages 565-590

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

Details

Published: 1973 Received: September 09, 1972 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: September 29, 2006 Reason for correction: - Correction: TITLE Details: Wrong : Semi-linear second-order elliptic equations in L¹
Right : Semi-linear second-order elliptic equations in L¹

Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: 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.

Date of correction: September 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

Corresponding author

Correction information

Register with J-STAGE for free!