Degenerate variational inequalities with gradient constraints
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 22 (1995) no. 1, p. 25-53
@article{ASNSP_1995_4_22_1_25_0,
author = {Choe, Hi Jun and Shim, Yong Sun},
title = {Degenerate variational inequalities with gradient constraints},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 22},
number = {1},
year = {1995},
pages = {25-53},
zbl = {0830.49005},
mrnumber = {1315349},
language = {en},
url = {http://www.numdam.org/item/ASNSP_1995_4_22_1_25_0}
}

Choe, Hi Jun; Shim, Yong Sun. Degenerate variational inequalities with gradient constraints. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 22 (1995) no. 1, pp. 25-53. http://www.numdam.org/item/ASNSP_1995_4_22_1_25_0/

[Br1] H. Brezis - D. Kinderlehrer, The Smoothness of Solutions to Nonlinear Variational Inequalities. Indiana Univ. Math. J. 23 (1974), 831-844. | MR 361436 | Zbl 0278.49011

[Br2] H. Brezis - G. Stampacchia, Sur la regularite de la solution d'inequations elliptiques. Bull. Soc. Math. France 96 (1968), 153-180. | Numdam | MR 239302 | Zbl 0165.45601

[Caf] L. Caffarelli - N.M. Riviere, The Lipschitz Character of the Stress Tensor When Twisting an Elastic and Plastic Bar. Arch. Rational Mech. Anal. 69 (1979), 31-36. | MR 513957 | Zbl 0399.73044

[Can] P Cannarsa - H.M. Soner, On the Singularities of the Viscosity Solutions to Hamilton-Jacobi-Bellman Equations. Indiana Univ. Math. J. 36 (1987), 501-524. | MR 905608 | Zbl 0612.70016

[Ch1] H.J. Choe, A regularity theory for a more general class of quasilinear elliptic partial differential equations and obstacle problems. Arch. Rational Mech. Anal. 114 (1991), 383-394. | MR 1100802 | Zbl 0733.35024

[Ch2] H.J. Choe - Y.S. Shim, On the variational inequalities for certain convex function classes. To appear in J. Differential Equations. | MR 1310935 | Zbl 0809.49007

[Chi] M. Chipot, Variational Inequalities and Flow in Porous Media. Applied Mathematical Sciences, 52, Springer, Berlin 1984. | MR 747637 | Zbl 0544.76095

[DiB] E. Di Benedetto, C1,α local regularity of weak solutions of degenerate elliptic equations. Nonlinear Anal. 7 (1983), 827-850. | Zbl 0539.35027

[Eva] L.C. Evans, A Second Order Elliptic Equation with Gradient Constraint. Comm. Partial Differential Equations 4 (1979), 555-572. | MR 529814 | Zbl 0448.35036

[Fle] W.H. Fleming - P.E. Souganidis, Asymptotic series and the method of vanishing viscosity. Indiana Univ. Math. J. 35 (1986), 425-447. | MR 833404 | Zbl 0573.35034

[Ge1] C. Gerhardt, Regularity of Solutions of Nonlinear Variational Inequalities with a Gradient Bound as Constraint. Arch. Rational Mech. Anal. 58 (1975), 309-317. | MR 385296 | Zbl 0338.49009

[Ge2] C. Gerhardt, Regularity of Solutions of Nonlinear Variational Inequalities. Arch. Rational Mech. Anal. 52 (1973), 389-393. | MR 377262 | Zbl 0277.49003

[Gia] M. Giaquinta, Remarks on the regularity of weak solutions to some variational inequalities. Math. Z. 177 (1981), 15-31. | MR 611467 | Zbl 0438.35019

[GT] D. Gilbarg - N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition. Springer-Verlag, Berlin 1983. | MR 737190 | Zbl 0562.35001

[Har] P. Hartman - G. Stampacchia, On some nonlinear elliptic differential functional equations. Acta Math. 115 (1971), 271-310. | MR 206537 | Zbl 0142.38102

[IK] H. Ishii - S. Koike, Boundary regularity and uniqueness for an elliptic equation with gradient constraint. Comm. Partial Differential Equations 8 (1983), 317-346. | MR 693645 | Zbl 0538.35012

[Is1] H. Ishii, Perron's method for Hamilton-Jacobi equations. Preprint. | MR 894587 | Zbl 0697.35030

[Is2] H. Ishii, A simple, direct proof of uniqueness for solutions of the Hamilton-Jacobi equations of Eikonal type. Proc. Amer. Math. Soc. 100 (1987), 247-251. | MR 884461 | Zbl 0644.35017

[Jen] R. Jensen, Regularity for Elasto-Plastic Type Variational Inequality. Indiana Univ. Math. J. 32 (1983), 407-423. | MR 697646 | Zbl 0554.35052

[Kry] N.V. Krylov, Boundedly inhomogeneous elliptic and parabolic equations in a domain. (Russian). Izv. Akad. Nauk SSSR 147 (1983), 75-108. | MR 688919 | Zbl 0578.35024

[Lad] O.A. Ladyzhenskaya - N.N. Ural'Tzeva, Linear and Quasilinear Elliptic Equations. Academic Press, 1968. | MR 244627 | Zbl 0164.13002

[Lew] J. Lewis, Regularity of derivatives of solutions to certain degenerate elliptic equations. Indiana Univ. Math. J. 32 (1983), 849-858. | MR 721568 | Zbl 0554.35048

[Li1] G. Lieberman, Local and boundary regularity for some variational inequalities involving p-Laplacian-type operators. Preprint.

[Li2] G. Lieberman, The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tzeva for elliptic equations, Comm. Partial Differential Equations 16 (1991), 311-362. | MR 1104103 | Zbl 0742.35028

[Li3] G. Lieberman, Regularity of solutions to some degenerate double obstacle problems. Preprint. | MR 1129339 | Zbl 0767.35029

[Lin] F.H. Lin - Y. Li, Boundary C1,α regularity for variational inequalities. Comm. Pure Appl. Math. XLIV (1991), 715-732. | MR 1109377 | Zbl 0760.49022

[Lind] P. Lindquist, Regularity for the gradient of the solution to a nonlinear obstacle problem with degenerate ellipticity, Nonlinear Anal. 12 (1988), 1245-1255. | MR 969502

[Lio1] P.L. Lions, Generalized solutions of Hamilton-Jacobi equations. Research Notes in Mathematics, vol. 69, Pitman Advanced Publishing Program, 1982. | MR 667669 | Zbl 0497.35001

[Lio2] P.L. Lions, Resolution de Problèmes Elliptiques Quasilinéaires. Arch. Rational Mech. Anal. 74 (1980), 335-353. | MR 588033 | Zbl 0449.35036

[Mic] J. Michael - W. Ziemer, Interior regularity for solutions to obstacle problems, Nonlinear Anal. 10 (1986), 1427-1448. | MR 869551 | Zbl 0603.49006

[Mu1] J. Mu, Higher regularity of the solution to the p-Laplacian obstacle problem. Preprint. | MR 1165427 | Zbl 0765.49008

[Mu2] J. Mu - W. Ziemer, Smooth regularity of solutions of double obstacle problems involving degenerate elliptic equations. Preprint. | MR 1113109 | Zbl 0742.35010

[Nor] T. Norando, C1,α local regularity for a class of quasilinear elliptic variational inequalities. Boll. Un. Mat. Ital. 5 (1986), 281-291. | MR 897200 | Zbl 0639.49009

[To1] P. Tolksdorff, Regularity for a more general class of quasi-linear elliptic equations. J. Differential Equations 51 (1984), 126-150. | MR 727034 | Zbl 0488.35017

[To2] P. Tolksdorff, Everywhere regularity for some quasilinear systems with a lack of ellipticity. Ann. Mat. Pura Appl. 134 (1983), 241-266. | MR 736742 | Zbl 0538.35034

[Uhl] K. Uhlenbeck, Regularity for a class of nonlinear elliptic systems, Acta Math. 138 (1977), 219-240. | MR 474389 | Zbl 0372.35030

[Wi] M. Wiegner, The C1,1 -character of solutions of second order elliptic equations with gradient constraints. Comm. Partial Differential Equations 6 (1981), 361-371. | MR 607553 | Zbl 0458.35035