Bulletin of the American Mathematical Society

Closed operators and existence theorems in multidimensional problems of the calculus of variations

L. Cesari and P. Kaiser

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 80, Number 3 (1974), 473-478.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183535521

Mathematical Reviews number (MathSciNet)
MR0338872

Zentralblatt MATH identifier
0287.49004

Subjects
Primary: 49A25 49A50
Secondary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Citation

Cesari, L.; Kaiser, P. Closed operators and existence theorems in multidimensional problems of the calculus of variations. Bull. Amer. Math. Soc. 80 (1974), no. 3, 473--478. https://projecteuclid.org/euclid.bams/1183535521


Export citation

References

  • 1. L. Cesari, Existence theorems for problems of optimization with distributed and boundary controls, Proc. Internat. Congress of Math. (Nice, 1970), vol. 3, Gauthier-Villars, Paris, 1971, pp. 157-161.
  • 2. L. Cesari, Existence theorems for weak and usual optimal solutions in Lagrange problems with unilateral constraints. I, II, Trans. Amer. Math. Soc. 124 (1966), 369-412, 413-430. MR 34 #3392; 3393.
  • 3. L. Cesari, Existence theorems for optimal controls of the Mayer type, SIAM J. Control 6 (1968), 517-552. MR 39 #4722.
  • 4. L. Cesari, Seminormality and upper semicontinuity in optimal control, J. Optimization Theory Appl. 6 (1970), 114-137. MR 42 #5139.
  • 5. L. Cesari, Closure theorems for orientor fields and weak convergence, Arch. Rational Mech. Anal. (to appear).
  • 6. L. Cesari, Lower semicontinuity and lower closure theorems without seminormality conditions, Ann. Mat. Pura Appl. 98 (1974), 381-397.
  • 7. L. Cesari, A necessary and sufficient condition for lower semicontinuity, Bull. Amer. Math. Soc. 80 (1974), 467-472.
  • 8. L. Cesari and D. E. Cowles, Existence theorems for optimization problems with distributed and boundary controls, Arch. Rational Mech. Anal. 46 (1972), 321-355.
  • 9. L. Cesari and M. B. Suryanarayana, Closure theorems without seminormality conditions, J. Optimization Theory Appl. (to appear).
  • 10. D. E. Cowles, Upper semicontinuity properties of variable sets in optimal control, J. Optimization Theory Appl. 10 (1972), 222-236.
  • 11. N. Dunford and J. T. Schwartz, Linear operators. II. Spectral theory. Selfadjoint operators in Hilbert space, Interscience, New York, 1963. MR 32 #6181.
  • 12. P. Kaiser, Closed operators in problems of optimal control with distributed parameters (to appear).
  • 13. C. Kuratowski, Les fonctions semi-continues dans l'espace des ensembles fermés, Fund. Math. 18 (1932), 148-166.
  • 14. G. J. Minty, Monotone (nonlinear) operators in Hilbert space, Duke Math. J. 29 (1962), 341-346. MR 29 #6319.