Global regularity for solutions of the minimal surface equation with continuous boundary values
Williams, Graham H.
Annales de l'I.H.P. Analyse non linéaire, Tome 3 (1986), p. 411-429 / Harvested from Numdam
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Publié le : 1986-01-01
@article{AIHPC_1986__3_6_411_0,
     author = {Williams, Graham H.},
     title = {Global regularity for solutions of the minimal surface equation with continuous boundary values},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {3},
     year = {1986},
     pages = {411-429},
     mrnumber = {870863},
     zbl = {0627.49020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1986__3_6_411_0}
}

Williams, Graham H. Global regularity for solutions of the minimal surface equation with continuous boundary values. Annales de l'I.H.P. Analyse non linéaire, Tome 3 (1986) pp. 411-429. http://gdmltest.u-ga.fr/item/AIHPC_1986__3_6_411_0/

[GG] M. Giaquinta, E. Giusti, Global C1,α-regularity for second-order quasilinear elliptic equations in divergence form. Preprint. J. Reine Angew. Math., t. 351, 1984, p. 55-65. | MR 749677 | Zbl 0528.35014

[GT] D. Gilbarg, N. Trudinger, Elliptic partial differential equations of second order. Springer-Verlag, Heidelberg, New York, 1977. | MR 473443 | Zbl 0361.35003

[G1] E. Giusti, Superfici cartesiane di are minima. Rend. Sem. Mat. Fis. Milano, t. 40, 1970, p. 135-153. | MR 291963 | Zbl 0219.53008

[G2] E. Giusti, Boundary behaviour of non-parametric minimal surfaces. Indiana Univ. Math. J., t. 22, 1972, p. 435-444. | MR 305253 | Zbl 0262.35020

[G3] E. Giusti, Minimal surfaces and functions of bounded variation. Birkhaüser-Boston Inc. 1984. | MR 775682 | Zbl 0545.49018

[JS] H. Jenkins, J. Serrin, The Dirichlet problem for the minimal surface equation in higher dimensions. J. Reine Angew. Math., t. 229, 1968, p. 170-187. | MR 222467 | Zbl 0159.40204

[L1] G. Lieberman, The quasilinear Dirichlet problem with decreased regularity at the boundary. Comm. Part. Diff. Equats, t. 6, 1981, p. 437-497. | MR 612553 | Zbl 0458.35039

[L2] G. Lieberman, The Dirichlet problem for quasilinear elliptic equations with Hölder continuous boundary values. Arch. Rat. Mech. Anal., t. 79, 1982, p. 305-323. | MR 656797 | Zbl 0497.35010

[L3] G. Liebermann, The Dirichlet problem for quasilinear elliptic equations with continuously differentiable boundary data. Preprint. Comm. Partial Differential Equations, t. 11, 1986, p. 167-229. | MR 818099 | Zbl 0589.35036

[L0] G. Lorentz, Approximation of functions. Holt, Rinehart and Winston, New York, 1966. | MR 213785 | Zbl 0153.38901

[M] K. Miller, Extremal barriers on cones with Phragmèn-Lindelöf theorems and other applications. Ann. Mat. Pura Appl. (4), t. 90, 1971, p. 297-329. | MR 316884 | Zbl 0231.35004

[S1] L. Simon, Global estimates of Hölder continuity for a class of divergence-form elliptic equations. Arch. Rat. Mech. Anal., t. 56, 1974, p. 253-272. | MR 352696 | Zbl 0295.35027

[S2] L. Simon, Boundary behaviour of solutions of the nonparametric least area problem. Bull. Austral. Math. Soc., t. 26, 1982, p. 17-27. | MR 679917 | Zbl 0499.49023

[S3] L. Simon, Personal communication.

[W1] G. Williams, Solutions of the minimal surface equation continuous and discontinuous at the boundary. Preprint. To appear. Comm. Partial Differential Equations. | MR 862695 | Zbl 0605.49030

[W2] G. Williams, The Dirichlet problem for the minimal surface equation with Lipschitz continuous boundary data. To appear. J. Reine Angew. Math., t. 354, 1984, p. 123-140. | MR 767575 | Zbl 0541.35033