Regularity of solutions for arbitrary order variational inequalities with general convex sets
Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) no. 6, pp. 719-758.
@article{AIHPC_1997__14_6_719_0,
author = {Liang, Jin},
title = {Regularity of solutions for arbitrary order variational inequalities with general convex sets},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {719--758},
publisher = {Gauthier-Villars},
volume = {14},
number = {6},
year = {1997},
zbl = {0911.49023},
mrnumber = {1482900},
language = {en},
url = {www.numdam.org/item/AIHPC_1997__14_6_719_0/}
}
Liang, Jin. Regularity of solutions for arbitrary order variational inequalities with general convex sets. Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) no. 6, pp. 719-758. http://www.numdam.org/item/AIHPC_1997__14_6_719_0/

[1] R.A. Adams, Sobolev Spaces, Academic Press, 1975. | MR 450957 | Zbl 0314.46030

[2] D.R. Adams and N.G. Meyers, Bessel Potentials, Inclusion Relations among Classes of Exceptional Sets, Indiana Univ. Math. J., Vol. 22, 1973, pp. 873-905. | MR 320346 | Zbl 0285.31007

[3] H. Attouch, Variational Convergence for Functions and Operators, Pitman Publishing, 1984. | MR 773850 | Zbl 0561.49012

[4] M.F. Bidaut-Veron, Variational Inequalities of Order 2m in Unbounded Domains, Nonlinear Anal., Th. Meth. and Appl., Vol. 6, 1982, pp. 253-269. | MR 654317 | Zbl 0491.35035

[5] M. Biroli, H2,p-Regularity for the Solution of Systems of Elliptic Variational Inequalities, Riv. Mat. Univ. Parma, Vol. 8, (4), 1982, pp. 539-547. | MR 706876 | Zbl 0527.35033

[6] L. Boccardo, An Ls-Estimate for the Gradient of Solutions of Some Nonlinear Unilateral Problems, Annali Mat. Pura ed Appl., Vol. 141, 1985, pp. 277-287. | MR 816788 | Zbl 0599.49009

[7] H. Brézis, Multiplicateur de Lagrange en Torsion Elasto-Plastique, Arch. Rat. Mech. Analysis, Vol. 49, 1972, pp. 32-40. | MR 346346 | Zbl 0265.35021

[8] L. Caffarelli, A. Friedman and A. Torelli, The Free Boundary for Fourth Order Variational Inequality, Illinois J. of Math., Vol. 25, 1981, pp. 402-422. | MR 620427 | Zbl 0466.35070

[9] J.I. Díaz, Nonlinear Partial Differential Equations and Free Boundaries (Volume I), Elliptic Equations, Research Notes in Mathematics, Vol. 106, Pitman Advanced Publishing Program, 1985. | MR 853732 | Zbl 0595.35100

[10] A. Friedman, Variational Principles and Free Boundary Problems, Wiley-Interscience, 1982. | MR 679313 | Zbl 0564.49002

[11] F.W. Gehring, The Lp-integrability of the Partial Derivatives of a Quasiconformal Mapping, Acta Math., Vol. 130, 1973, pp. 265-277. | MR 402038 | Zbl 0258.30021

[12] C. Gerhardt, On the Capillarity Problem with Constant Volume, Ann. Sc. Norm. Sup. Pisa, Vol. 2, 1975, pp. 303-320. | Numdam | MR 390897 | Zbl 0321.76010

[13] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton University Press, 1983. | MR 717034 | Zbl 0516.49003

[14] M. Giaquinta and G. Modica, Regularity Results for Some Classes of Higher Order Nonlinear Elliptic Systems, J. Reine Angew. Math., Vol. 311/312, 1979, pp. 145-169. | MR 549962 | Zbl 0409.35015

[15] S. Hildebrandt and K.-O. Widman, Variational Inequalities for Vectorvalued Functions, J. Reine. Ange. Math., Vol. 309, 1979, pp. 191-219. | MR 542048 | Zbl 0408.49012

[16] R. Jensen, Regularity for Elasto-Plastic Type Variational Inequalities, Indiana Univ. Math. J., Vol. 32, 1983, pp. 407-423. | MR 697646 | Zbl 0554.35052

[17] J. Liang, Regularity of Elliptic Systems by Blow - up method, Bollettino U.M.I., Vol. 6, 5-A, 1986, pp. 443-448. | MR 866555 | Zbl 0608.35016

[18] J. Liang, Convergence of a Sequence of Closed Convex Sets with Parameters and Some Concrete Cases of Structures, to appear.

[19] J. Liang and L. Santos, On a Kind of Nonlinear High Order Variational Inequality System, Differential and Integral Equations, Vol. 6, 1993, pp. 1519-1530. | MR 1235209 | Zbl 0789.49004

[20] J. Liang and L. Santos, Convergence in Mosco Sense for Sequences of Some General Concrete Convex Sets, preprint.

[21] J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Paris, 1969. | MR 259693 | Zbl 0189.40603

[22] V.G. Maz'Ja, Sobolev Spaces, Springer-Verlag, 1985. | MR 817985

[23] N.G. Meyers and A. Elcrat, Some Results on Regularity for Solutions of Non-linear Elliptic Systems and Quasi-Regular Functions, Duke Math. J., Vol. 42, 1975, pp. 121-136. | MR 417568 | Zbl 0347.35039

[24] U. Mosco, Approximations of the Solutions of Some Variational Inequalities, Ann. Sc. Norm. Sup. Pisa, Vol. 21, 1967, pp. 373-394. | Numdam | MR 226376 | Zbl 0184.36803

[25] U. Mosco, Convergence of Convex Sets and of Solutions of Quasi-Variational Inequalities, Adv. Math., Vol. 3, 1969, pp. 510-585. | MR 298508 | Zbl 0192.49101

[26] L. Nirenberg, An Extended Interpolation Inequality, Ann. Sc. Norm. Sup. Pisa, Vol. 20, 1966, pp. 733-737. | Numdam | MR 208360 | Zbl 0163.29905

[27] J.F. Rodrigues, Obstacle Problems in Mathematical Physics, Elsevier Science Publishers B.V., 1987. | MR 880369 | Zbl 0606.73017

[28] K. Yosida, Functional Analysis, Springer-Verlag, 1965. | Zbl 0126.11504