| Title:
|
On general boundary value problems and duality in linear elasticity. II (English) |
| Author:
|
Hünlich, Rolf |
| Author:
|
Naumann, Joachim |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
25 |
| Issue:
|
1 |
| Year:
|
1980 |
| Pages:
|
11-32 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
general boundary value problems |
| Keyword:
|
principle of minimum potential energy |
| Keyword:
|
existence theorems |
| Keyword:
|
dual problem |
| MSC:
|
35J20 |
| MSC:
|
49S05 |
| MSC:
|
73C02 |
| MSC:
|
74B99 |
| MSC:
|
74H99 |
| idZBL:
|
Zbl 0453.73013 |
| idMR:
|
MR0554088 |
| DOI:
|
10.21136/AM.1980.103834 |
| . |
| Date available:
|
2008-05-20T18:13:28Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103834 |
| . |
| Reference:
|
[1] Duvaut G., Lions J. L.: Les inéquations en mécanique et en physique.Dunod, Paris 1972. Zbl 0298.73001, MR 0464857 |
| Reference:
|
[2] Ekeland I., Temam R.: Analyse convexe et problèmes variationnels.Dunod, Gauthier- Villars, Paris 1974. Zbl 0281.49001, MR 0463993 |
| Reference:
|
[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. MR 0178631 |
| Reference:
|
[4] Fichera G.: Boundary value problems of elasticity with unilateral constraints.In: Handbuch der Physik (Herausg.: S. Flügge), Band VI a/2, Springer, 1972. |
| Reference:
|
[5] Gajewski H., Gröger K.: Konjugierte Operatoren und a-posteriori-Fehlerabschützungen.Math. Nachr. 73 (1976), ЗІ5-333. MR 0435959, 10.1002/mana.19760730124 |
| Reference:
|
[6] Hess P.: On semi-coercive nonlinear problems.Indiana Univ. Math. J., 23 (1974), 645-654. Zbl 0259.47051, MR 0341214, 10.1512/iumj.1974.23.23055 |
| Reference:
|
[7] Hlaváček I.: Variational principles in the linear theory of elasticity for general boundary conditions.Apl. Matem., 12 (1967), 425 - 447. MR 0231575 |
| Reference:
|
[8] Hlaváček I., Nečas J.: On inequalities of Korn's type. II: Applications to linear elasticity.Arch. Rat. Mech. Anal., 36 (1970), 312-334. Zbl 0193.39002, MR 0252845, 10.1007/BF00249519 |
| Reference:
|
[9] Ioffe A. D., Tikhomirov V. M.: The theory of extremum problems.(Russian). Moscow, 1974. |
| Reference:
|
[10] Krein S. G.: Linear equations in a Banach space.(Russian). Moscow, 1971. MR 0374949 |
| Reference:
|
[11] Lions J. L., Stampacchia G.: Variational inequalities.Comm. Pure Appl. Math., 20 (1967), 493-519. Zbl 0152.34601, MR 0216344, 10.1002/cpa.3160200302 |
| Reference:
|
[12] Nayroles B.: Duality and convexity in solid equilibrium problems.Laboratoire Méc. et d'Accoustique, C.N.R.S., Marseille 1974. |
| Reference:
|
[13] Rockafellar R. T.: Duality and stability in extremum problems involving convex functions.Pacific J. Math., 21 (1967), 167-187. Zbl 0154.44902, MR 0211759, 10.2140/pjm.1967.21.167 |
| Reference:
|
[14] Schatzman M.: Problèmes aux limites non linéaires, non coercifs.Ann. Scuola Norm. Sup. Pisa, 27, serie III (1973), 640-686. MR 0380545 |
| . |
