| Title:
|
Inequalities of Korn's type, uniform with respect to a class of domains (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1989 |
| Pages:
|
105-112 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Inequalities of Korn's type involve a positive constant, which depends on the domain, in general. A question arises, whether the constants possess a positive infimum, if a class of bounded two-dimensional domains with Lipschitz boundary is considered. The proof of a positive answer to this question is shown for several types of boundary conditions and for two classes of domains. (English) |
| Keyword:
|
domain optimization |
| Keyword:
|
Korn’s inequality |
| Keyword:
|
Friedrichs inequality |
| MSC:
|
35J20 |
| MSC:
|
35J55 |
| MSC:
|
49A22 |
| MSC:
|
49J20 |
| idZBL:
|
Zbl 0673.49003 |
| idMR:
|
MR0990298 |
| DOI:
|
10.21136/AM.1989.104339 |
| . |
| Date available:
|
2008-05-20T18:36:12Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104339 |
| . |
| Reference:
|
[1] J. Haslinger P. Neittaanmäki T. Tiihonen: Shape optimization of an elastic body in contact based on penalization of the state.Apl. Mat. 31 (1986), 54-77. MR 0836802 |
| Reference:
|
[2] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction.Elsevier, Amsterdam, 1981. MR 0600655 |
| Reference:
|
[3] I. Hlaváček J. Nečas: On inequalities of Korn's type.Arch. Ratl. Mech. Anal. 36 (1970), 305-334. MR 0252844, 10.1007/BF00249518 |
| Reference:
|
[4] J. A. Nitsche: On Korn's second inequality.R.A.I.R.O. Anal. numer., 15 (1981), 237-248. Zbl 0467.35019, MR 0631678 |
| Reference:
|
[5] T. Tiihonen: On Korn's inequality and shape optimization.Preprint No. 61, University of Jyväskylä, April 1987. MR 0893392 |
| . |
