| Title:
|
Noncoercive hemivariational inequality and its applications in nonconvex unilateral mechanics (English) |
| Author:
|
Goeleven, Daniel |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
41 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
203-229 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper is devoted to the study of a class of hemivariational inequalities which was introduced by P. D. Panagiotopoulos [31] and later by Z. Naniewicz [22]. These variational formulations are natural nonconvex generalizations [15–17], [22–33] of the well-known variational inequalities. Several existence results are proved in [15]. In this paper, we are concerned with some related results and several applications. (English) |
| Keyword:
|
hemivariational inequalities |
| Keyword:
|
variational inequalities |
| Keyword:
|
abstract set-valued law in mechanics |
| Keyword:
|
star-shaped admissible sets |
| MSC:
|
49J40 |
| MSC:
|
49J52 |
| idZBL:
|
Zbl 0863.49007 |
| idMR:
|
MR1382465 |
| DOI:
|
10.21136/AM.1996.134321 |
| . |
| Date available:
|
2009-09-22T17:51:07Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134321 |
| . |
| Reference:
|
[1] R. A. Adams: Sobolev Spaces.Academic Press, New York, 1975. Zbl 0314.46030, MR 0450957 |
| Reference:
|
[2] S. Adly, D. Goeleven, M. Théra: Recession mappings and noncoercive variational inequalities.(to appear). MR 1377476 |
| Reference:
|
[3] H. Attouch, Z. Chbani, A. Moudafi: Recession operators and solvability of variational problems.Preprint, Laboratoire d’Analyse Convexe, Université de Montpellier 1993. |
| Reference:
|
[4] C. Baiocchi, G. Buttazzo, F. Gastaldi, F. Tomarelli: General existence theorems for unilateral problems in continuum mechanics.Arch. Rat. Mech. Anal. 100 (1988), no. 2, 149–180. MR 0913962, 10.1007/BF00282202 |
| Reference:
|
[5] H. Brézis, L. Nirenberg: Characterizations of the ranges of some nonlinear operators and applications to boundary value problems.Ann. Scuola Normale Superiore Pisa, Classe di Scienze Serie IV V (1978), no. 2, 225–235. MR 0513090 |
| Reference:
|
[6] F. E. Browder: Nonlinear operators and nonlinear equations of evolution in Banach spaces.Proceedings of Symposia in Pure Mathematics, Amer. Math. Soc. XVIII (1976), no. 2. Zbl 0327.47022, MR 0405188 |
| Reference:
|
[7] P. G. Ciarlet, P. Rabier: Les équations de Von Karman.Lecture Notes in Mathematics 836, Springer Verlag, 1980. MR 0595326 |
| Reference:
|
[8] P. G. Ciarlet, J. Nečas: Unilateral problems in nonlinear three-dimensional elasticity.Arch. Rational Mech. Anal. 87 (1985), 319–338. MR 0767504, 10.1007/BF00250917 |
| Reference:
|
[9] A. Cimetière: Un problème de flambement Unilatéral en théorie des plaques.Journal de Mécanique 19 (1980), no. 1, 183–202. MR 0571805 |
| Reference:
|
[10] F. H. Clarke: Nonsmooth Analysis and Optimization.Wiley, New York, 1984. |
| Reference:
|
[11] J. Dieudonné: Eléments d’Analyse.Gauthier-Villars, 1968. |
| Reference:
|
[12] G. Fichera: Boundary value problems in elasticity with unilateral constraints.Handbuch der Physik, Springer-verlag, Berlin-Heidelberg-New York VIa.2 (1972), 347–389. |
| Reference:
|
[13] J. Frehse: Capacity methods in the theory of partial differential equations.Iber. d. Dt. Math.-Verein 84 (1982), 1–44. Zbl 0486.35002, MR 0644068 |
| Reference:
|
[14] D. Goeleven: On the solvability of noncoercive linear variational inequalities in separable Hilbert spaces.Journal of Optimization Theory and Applications 79 (1993), no. 3, 493–511. Zbl 0798.49012, MR 1255283, 10.1007/BF00940555 |
| Reference:
|
[15] D. Goeleven: Noncoercive hemivariational inequality approach to constrained problems for star-shaped admissible sets.FUNDP Research-Report, 1994. |
| Reference:
|
[16] D. Goeleven, G. E. Stavroulakis, P. D. Panagiotopoulos: Solvability theory for a class of hemivariational inequalities involving copositive plus matrices.Applications in Robotics, Preprint 1995. MR 1422180 |
| Reference:
|
[17] H. N. Karamanlis, P. D. Panagiotopoulos: The eigenvalue problems in hemivariational inequalities and its applications to composite plates.Journal Mech. Behaviour of Materials, To appear. |
| Reference:
|
[18] N. Kikuchi, J. T. Oden: Contact problems in elasticity: A study of variational inequalities and finite element methods.SIAM, Philadelphia, 1988. MR 0961258 |
| Reference:
|
[19] E. M. Landesman, A. C. Lazer: Nonlinear perturbations of linear elliptic boundary value problems at resonance.Journal of Mathematics and Mechanics 19 (1970), 609–623. MR 0267269 |
| Reference:
|
[20] J. L. Lions, G. Stampacchia: Variational inequalities.Comm. Pure Applied Math. XX (1967), 493–519. MR 0216344, 10.1002/cpa.3160200302 |
| Reference:
|
[21] D. T. Luc, J-P. Penot: Convergence of Asymptotic Directions.Preprint Université de Pau, 1994. |
| Reference:
|
[22] Z. Naniewicz: Hemivariational inequality approach to constrained problems for starshaped admissible sets.Journal of Optimization Theory and Applications 83 (1994), no. 1, 97–112. MR 1298859, 10.1007/BF02191764 |
| Reference:
|
[23] Z. Naniewicz: On the pseudo-monotonocity of generalized gradients of nonconvex functions.Applicable Analysis 47 (1992), 151–172. MR 1333952, 10.1080/00036819208840138 |
| Reference:
|
[24] P. D. Panagiotopoulos: Coercive and semicoercive hemivariational inequalities.Nonlinear Analysis, Theory, Methods & Applications 16 (1991), no. 3, 209–231. Zbl 0733.49012, MR 1091520, 10.1016/0362-546X(91)90224-O |
| Reference:
|
[25] P. D. Panagiotopoulos: Inéquations Hémivariationnelles semi-coercives dans la théorie des plaques de Von Karman.C. R. Acad. Sci. Paris 307 (1988), no. Série I, 735–738. Zbl 0653.73011, MR 0972823 |
| Reference:
|
[26] P. D. Panagiotopoulos, G. E. Stravoulakis: The delamination effect in laminated Von Kármán plates under unilateral boundary conditions. A variational-hemivariational inequality approach.Journal of Elasticity 23 (1990), 69–96. MR 1065231, 10.1007/BF00041685 |
| Reference:
|
[27] P. D. Panagiotopoulos, G. E. Stravoulakis: A variational-hemivariational inequality approach to the laminated plate theory under subdifferential boundary conditions.Quarterly of Applied Mathematics XLVI (1988), no. 3, 409–430. MR 0963579, 10.1090/qam/963579 |
| Reference:
|
[28] P. D. Panagiotopoulos: Semicoercive hemivariational inequalities, on the delamination of composite plates.Quarterly of Applied Mathematics XLVII (1989), no. 4, 611–629. Zbl 0693.73007, MR 1031680 |
| Reference:
|
[29] P. D. Panagiotopoulos: Hemivariational inequalities and substationarity in the static theory of v. Kármán plates.ZAMM, Z. Angew. Math. u. Mech. 65 (1985), no. 6, 219–229. MR 0801713, 10.1002/zamm.19850650608 |
| Reference:
|
[30] P. D. Panagiotopoulos: Hemivariational inequalities and their applications.In: J. J. Moreau, P. D. Panagiotopoulos, G. Strang (eds), Topics in Nonsmooth Mechanics, Birkhäuser Verlag 1988. Zbl 0973.90060, MR 0957088 |
| Reference:
|
[31] P. D. Panagiotopoulos: Nonconvex superpotentials in the sense of F. H. Clarke and applications.Mech. Res. Comm. 8 (1981), 335–340. MR 0639382 |
| Reference:
|
[32] P. D. Panagiotopoulos: Nonconvex Energy Function, Hemivariational Inequalities and Substationarity Principles.Acta Mech. 48 (1983), 160–183. MR 0715806 |
| Reference:
|
[33] P. D. Panagiotopoulos: Hemivariational Inequalities, Applications in Mechanics and Engineering.Springer Verlag Berlin Heidelberg, 1993. Zbl 0826.73002, MR 1385670 |
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