| Title:
|
Von Kármán equations. III. Solvability of the von Kármán equations with conditions for geometry of the boundary of the domain (English) |
| Author:
|
Cibula, Július |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
36 |
| Issue:
|
5 |
| Year:
|
1991 |
| Pages:
|
368-379 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Solvability of the general boundary value problem for von Kármán system of nonlinear equations is studied. The problem is reduced to an operator equation. It is shown that the corresponding functional of energy is coercive and weakly lower semicontinuous. Then the functional of energy attains absolute minimum which is a variational solution of the problem. (English) |
| Keyword:
|
variational solution |
| Keyword:
|
Sobolev space |
| Keyword:
|
linear continuous functional |
| Keyword:
|
operator, curvature |
| Keyword:
|
property of coerciveness |
| Keyword:
|
weakly lower semicontinuous functional |
| Keyword:
|
absolute minimum |
| Keyword:
|
functional of energy |
| MSC:
|
35D05 |
| MSC:
|
35G30 |
| MSC:
|
35Q99 |
| MSC:
|
73C50 |
| MSC:
|
73K10 |
| MSC:
|
74B20 |
| MSC:
|
74K20 |
| MSC:
|
74P10 |
| MSC:
|
74S30 |
| idZBL:
|
Zbl 0754.73035 |
| idMR:
|
MR1125638 |
| DOI:
|
10.21136/AM.1991.104473 |
| . |
| Date available:
|
2008-05-20T18:42:16Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104473 |
| . |
| Reference:
|
[1] J. Cibula: Equations de von Kármán. I. Résultat d'existence pour les problèmes aux limites non homogènes.Aplikace matematiky, 29 (1984), 317-332. Zbl 0575.35034, MR 0772267 |
| Reference:
|
[2] J. Cibula: Equations de von Kármán. II. Approximation de la solution.Aplikace matematiky, 30(1985), 1-10. Zbl 0606.35031, MR 0779329 |
| Reference:
|
[3] J. Céa: Optimisation, théorie et algoritmes.Dunod, Paris 1971. MR 0298892 |
| Reference:
|
[4] P. G. Ciarlet P. Rabier: Lés équations de von Kármán.Lecture Notes in Math., vol. 826. Springer-Verlag, Berlin-Heidelberg-New York 1980. MR 0595326 |
| Reference:
|
[5] I. Hlaváček J. Naumann: Inhomogeneous boundary value problems for the von Kármán equation, I.Aplikace matematiky 19 (1974), 253-269. MR 0377307 |
| Reference:
|
[6] O. John J. Nečas: On the solvability of von Kármán equations.Aplikace matematiky, 20 (1975), 48-62. MR 0380099 |
| Reference:
|
[7] G. H. Knightly: An existence theorem for the von Kármán equations.Arch. Rat. Mech. Anal., 27 (1967), 233-242. Zbl 0162.56303, MR 0220472, 10.1007/BF00290614 |
| Reference:
|
[8] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584 |
| . |
