Keywords: hemivariational inequalities; variational inequalities; abstract set-valued law in mechanics; star-shaped admissible sets
@article{10_21136_AM_1996_134321,
author = {Goeleven, Daniel},
title = {Noncoercive hemivariational inequality and its applications in nonconvex unilateral mechanics},
journal = {Applications of Mathematics},
pages = {203--229},
year = {1996},
volume = {41},
number = {3},
doi = {10.21136/AM.1996.134321},
mrnumber = {1382465},
zbl = {0863.49007},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1996.134321/}
}
TY - JOUR AU - Goeleven, Daniel TI - Noncoercive hemivariational inequality and its applications in nonconvex unilateral mechanics JO - Applications of Mathematics PY - 1996 SP - 203 EP - 229 VL - 41 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.21136/AM.1996.134321/ DO - 10.21136/AM.1996.134321 LA - en ID - 10_21136_AM_1996_134321 ER -
%0 Journal Article %A Goeleven, Daniel %T Noncoercive hemivariational inequality and its applications in nonconvex unilateral mechanics %J Applications of Mathematics %D 1996 %P 203-229 %V 41 %N 3 %U http://geodesic.mathdoc.fr/articles/10.21136/AM.1996.134321/ %R 10.21136/AM.1996.134321 %G en %F 10_21136_AM_1996_134321
Goeleven, Daniel. Noncoercive hemivariational inequality and its applications in nonconvex unilateral mechanics. Applications of Mathematics, Tome 41 (1996) no. 3, pp. 203-229. doi: 10.21136/AM.1996.134321
[1] R. A. Adams: Sobolev Spaces. Academic Press, New York, 1975. | MR | Zbl
[2] S. Adly, D. Goeleven, M. Théra: Recession mappings and noncoercive variational inequalities. (to appear). | MR
[3] H. Attouch, Z. Chbani, A. Moudafi: Recession operators and solvability of variational problems. Preprint, Laboratoire d’Analyse Convexe, Université de Montpellier 1993.
[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. | DOI | MR
[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
[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. | MR | Zbl
[7] P. G. Ciarlet, P. Rabier: Les équations de Von Karman. Lecture Notes in Mathematics 836, Springer Verlag, 1980. | MR
[8] P. G. Ciarlet, J. Nečas: Unilateral problems in nonlinear three-dimensional elasticity. Arch. Rational Mech. Anal. 87 (1985), 319–338. | DOI | MR
[9] A. Cimetière: Un problème de flambement Unilatéral en théorie des plaques. Journal de Mécanique 19 (1980), no. 1, 183–202. | MR
[10] F. H. Clarke: Nonsmooth Analysis and Optimization. Wiley, New York, 1984.
[11] J. Dieudonné: Eléments d’Analyse. Gauthier-Villars, 1968.
[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.
[13] J. Frehse: Capacity methods in the theory of partial differential equations. Iber. d. Dt. Math.-Verein 84 (1982), 1–44. | MR | Zbl
[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. | DOI | MR | Zbl
[15] D. Goeleven: Noncoercive hemivariational inequality approach to constrained problems for star-shaped admissible sets. FUNDP Research-Report, 1994.
[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
[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.
[18] N. Kikuchi, J. T. Oden: Contact problems in elasticity: A study of variational inequalities and finite element methods. SIAM, Philadelphia, 1988. | MR
[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
[20] J. L. Lions, G. Stampacchia: Variational inequalities. Comm. Pure Applied Math. XX (1967), 493–519. | DOI | MR
[21] D. T. Luc, J-P. Penot: Convergence of Asymptotic Directions. Preprint Université de Pau, 1994.
[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. | DOI | MR
[23] Z. Naniewicz: On the pseudo-monotonocity of generalized gradients of nonconvex functions. Applicable Analysis 47 (1992), 151–172. | DOI | MR
[24] P. D. Panagiotopoulos: Coercive and semicoercive hemivariational inequalities. Nonlinear Analysis, Theory, Methods & Applications 16 (1991), no. 3, 209–231. | DOI | MR | Zbl
[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. | MR | Zbl
[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. | DOI | MR
[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. | DOI | MR
[28] P. D. Panagiotopoulos: Semicoercive hemivariational inequalities, on the delamination of composite plates. Quarterly of Applied Mathematics XLVII (1989), no. 4, 611–629. | MR | Zbl
[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. | DOI | MR
[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. | MR | Zbl
[31] P. D. Panagiotopoulos: Nonconvex superpotentials in the sense of F. H. Clarke and applications. Mech. Res. Comm. 8 (1981), 335–340. | MR
[32] P. D. Panagiotopoulos: Nonconvex Energy Function, Hemivariational Inequalities and Substationarity Principles. Acta Mech. 48 (1983), 160–183. | MR
[33] P. D. Panagiotopoulos: Hemivariational Inequalities, Applications in Mechanics and Engineering. Springer Verlag Berlin Heidelberg, 1993. | MR | Zbl
Cité par Sources :