Pacific Journal of Mathematics

Basic calculus of variations.

Edward Silverman

Article information

Source
Pacific J. Math., Volume 104, Number 2 (1983), 471-482.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102723676

Mathematical Reviews number (MathSciNet)
MR684304

Zentralblatt MATH identifier
0515.49007

Subjects
Primary: 49A50

Citation

Silverman, Edward. Basic calculus of variations. Pacific J. Math. 104 (1983), no. 2, 471--482. https://projecteuclid.org/euclid.pjm/1102723676


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References

  • [1] J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal., 63 (1977), 337-403.
  • [2] Lamberto Cesari, An existence theorem of calculus of variations on parametric surfaces, Amer. J. Math, 74 (1952), 265-295.
  • [3] Lamberto Cesari, Surface Area, Princeton Press, 1956.
  • [4] Lamberto Cesari, A necessary and sufficient conditionfor lower semicontinuity, Bull. Amer. Math. Soc, 80 (1974), 467-472.
  • [5] C. B. Morrey, Jr., Quasi-convexity and the lower semicontinuity of multiple integrals, Pacific J. Math, 2 (1952), 25-53.
  • [6] C. B. Morrey, Multiple Integrals in the Calculus of Variations, Springer Verlag Vol. 130, 1966.
  • [7] Edward Silverman, A sufficient condition for the lower semicontinuity of parametric integrals, Trans. Amer. Math. Soc, 167 (1972), 465-469.
  • [8] Edward Silverman, Lower semicontinuity of parametric integrals, Trans. Amer. Math. Soc, 175 (1973), 499-508.
  • [9] Edward Silverman, Strong quasi-convexity, Pacific J. Math, 46 (1973), 549-554.
  • [10] L. H. Turner, The direct method in the calculus of variations, Purdue Thesis, 1957.

See also

  • Remarks on : J. M. Ball. Remarks on the paper: ``Basic calculus of variations''. Pacific Journal of Mathematics volume 116, issue 1, (1985), pp. 7-10.