On general boundary value problems and duality in linear elasticity. II

Rolf Hünlich; Joachim Naumann

Aplikace matematiky (1980)

  • Volume: 25, Issue: 1, page 11-32
  • ISSN: 0862-7940

Abstract

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The present part of the paper completes the discussion in Part I in two directions. Firstly, in Section 5 a number of existence theorems for a solution to Problem III (principle of minimum potential energy) is established. Secondly, Section 6 and 7 are devoted to a discussion of both the classical and the abstract approach to the duality theory as well as the relationship between the solvability of Problem III and its dual one.

How to cite

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Hünlich, Rolf, and Naumann, Joachim. "On general boundary value problems and duality in linear elasticity. II." Aplikace matematiky 25.1 (1980): 11-32. <http://eudml.org/doc/15127>.

@article{Hünlich1980,
abstract = {The present part of the paper completes the discussion in Part I in two directions. Firstly, in Section 5 a number of existence theorems for a solution to Problem III (principle of minimum potential energy) is established. Secondly, Section 6 and 7 are devoted to a discussion of both the classical and the abstract approach to the duality theory as well as the relationship between the solvability of Problem III and its dual one.},
author = {Hünlich, Rolf, Naumann, Joachim},
journal = {Aplikace matematiky},
keywords = {general boundary value problems; principle of minimum potential energy; existence theorems; dual problem; general boundary value problems; principle of minimum potential energy; existence theorems; dual problem},
language = {eng},
number = {1},
pages = {11-32},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On general boundary value problems and duality in linear elasticity. II},
url = {http://eudml.org/doc/15127},
volume = {25},
year = {1980},
}

TY - JOUR
AU - Hünlich, Rolf
AU - Naumann, Joachim
TI - On general boundary value problems and duality in linear elasticity. II
JO - Aplikace matematiky
PY - 1980
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 25
IS - 1
SP - 11
EP - 32
AB - The present part of the paper completes the discussion in Part I in two directions. Firstly, in Section 5 a number of existence theorems for a solution to Problem III (principle of minimum potential energy) is established. Secondly, Section 6 and 7 are devoted to a discussion of both the classical and the abstract approach to the duality theory as well as the relationship between the solvability of Problem III and its dual one.
LA - eng
KW - general boundary value problems; principle of minimum potential energy; existence theorems; dual problem; general boundary value problems; principle of minimum potential energy; existence theorems; dual problem
UR - http://eudml.org/doc/15127
ER -

References

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  2. Ekeland I., Temam R., Analyse convexe et problèmes variationnels, Dunod, Gauthier- Villars, Paris 1974. (1974) Zbl0281.49001MR0463993
  3. Fichera G., Problemi elastostatici con vincoli unilaterali: il problemadi Signorini con ambigue condizioni al contorno, Atti Accad. Naz. Lincei, Memorie (Cl. Sci. fis., mat. e nat.), serie 8, vol. 7 (1964), 91-140. (1964) Zbl0146.21204MR0178631
  4. Fichera G., Boundary value problems of elasticity with unilateral constraints, In: Handbuch der Physik (Herausg.: S. Flügge), Band VI a/2, Springer, 1972. (1972) 
  5. Gajewski H., Gröger K., 10.1002/mana.19760730124, Math. Nachr. 73 (1976), ЗІ5-333. (1976) Zbl0352.65025MR0435959DOI10.1002/mana.19760730124
  6. Hess P., 10.1512/iumj.1974.23.23055, Indiana Univ. Math. J., 23 (1974), 645-654. (1974) Zbl0259.47051MR0341214DOI10.1512/iumj.1974.23.23055
  7. Hlaváček I., Variational principles in the linear theory of elasticity for general boundary conditions, Apl. Matem., 12 (1967), 425 - 447. (1967) Zbl0153.55401MR0231575
  8. Hlaváček I., Nečas J., 10.1007/BF00249519, Arch. Rat. Mech. Anal., 36 (1970), 312-334. (1970) Zbl0193.39002MR0252845DOI10.1007/BF00249519
  9. Ioffe A. D., Tikhomirov V. M., The theory of extremum problems, (Russian). Moscow, 1974. (1974) Zbl0191.13101
  10. Krein S. G., Linear equations in a Banach space, (Russian). Moscow, 1971. (1971) MR0374949
  11. Lions J. L., Stampacchia G., 10.1002/cpa.3160200302, Comm. Pure Appl. Math., 20 (1967), 493-519. (1967) Zbl0152.34601MR0216344DOI10.1002/cpa.3160200302
  12. Nayroles B., Duality and convexity in solid equilibrium problems, Laboratoire Méc. et d'Accoustique, C.N.R.S., Marseille 1974. (1974) 
  13. Rockafellar R. T., 10.2140/pjm.1967.21.167, Pacific J. Math., 21 (1967), 167-187. (1967) Zbl0154.44902MR0211759DOI10.2140/pjm.1967.21.167
  14. Schatzman M., Problèmes aux limites non linéaires, non coercifs, Ann. Scuola Norm. Sup. Pisa, 27, serie III (1973), 640-686. (1973) Zbl0324.47031MR0380545

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