On the range of a coercive maximal monotone operator in a nonreflexive Banach space
HTML articles powered by AMS MathViewer
- by Jean-Pierre Gossez
- Proc. Amer. Math. Soc. 35 (1972), 88-92
- DOI: https://doi.org/10.1090/S0002-9939-1972-0298492-7
- PDF | Request permission
Abstract:
It is shown that the range of a coercive everywhere defined maximal monotone operator from a (nonreflexive) Banach space into its dual is dense for the $\mathrm {weak}^*$ topology but not necessarily for the norm topology.References
- Errett Bishop and R. R. Phelps, The support functionals of a convex set, Proc. Sympos. Pure Math., Vol. VII, Amer. Math. Soc., Providence, R.I., 1963, pp. 27–35. MR 0154092
- Haïm Brezis, On some degenerate nonlinear parabolic equations, Nonlinear Functional Analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 1, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 28–38. MR 0273468
- Felix E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Nonlinear functional analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1976, pp. 1–308. MR 0405188
- Felix E. Browder, Existence theory for boundary value problems for quasilinear elliptic systems with strongly nonlinear lower order terms, Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1973, pp. 269–286. MR 0340815
- Mahlon M. Day, Strict convexity and smoothness of normed spaces, Trans. Amer. Math. Soc. 78 (1955), 516–528. MR 67351, DOI 10.1090/S0002-9947-1955-0067351-1
- Thomas Donaldson, Nonlinear elliptic boundary value problems in Orlicz-Sobolev spaces, J. Differential Equations 10 (1971), 507–528. MR 298472, DOI 10.1016/0022-0396(71)90009-X
- Jean-Pierre Gossez, Opérateurs monotones non linéaires dans les espaces de Banach non réflexifs, J. Math. Anal. Appl. 34 (1971), 371–395 (French). MR 313890, DOI 10.1016/0022-247X(71)90119-3
- Jean-Pierre Gossez, On the subdifferential of a saddle function, J. Functional Analysis 11 (1972), 220–230. MR 0350416, DOI 10.1016/0022-1236(72)90092-4
- R. T. Rockafellar, On the maximal monotonicity of subdifferential mappings, Pacific J. Math. 33 (1970), 209–216. MR 262827
- R. T. Rockafellar, Monotone operators associated with saddle-functions and minimax problems, Nonlinear Functional Analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 1, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 241–250. MR 0285942
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 88-92
- MSC: Primary 47H05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0298492-7
- MathSciNet review: 0298492