Global regularity for solutions of the minimal surface equation with continuous boundary values

Graham H. Williams

Annales de l'I.H.P. Analyse non linéaire (1986)

  • Volume: 3, Issue: 6, page 411-429
  • ISSN: 0294-1449

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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 3.6 (1986): 411-429. <http://eudml.org/doc/78121>.

@article{Williams1986,
author = {Williams, Graham H.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Hölder continuity; Dirichlet problem; minimal surface equation; barriers},
language = {eng},
number = {6},
pages = {411-429},
publisher = {Gauthier-Villars},
title = {Global regularity for solutions of the minimal surface equation with continuous boundary values},
url = {http://eudml.org/doc/78121},
volume = {3},
year = {1986},
}

TY - JOUR
AU - Williams, Graham H.
TI - Global regularity for solutions of the minimal surface equation with continuous boundary values
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1986
PB - Gauthier-Villars
VL - 3
IS - 6
SP - 411
EP - 429
LA - eng
KW - Hölder continuity; Dirichlet problem; minimal surface equation; barriers
UR - http://eudml.org/doc/78121
ER -

References

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  1. [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. Zbl0528.35014MR749677
  2. [GT] D. Gilbarg, N. Trudinger, Elliptic partial differential equations of second order. Springer-Verlag, Heidelberg, New York, 1977. Zbl0361.35003MR473443
  3. [G1] E. Giusti, Superfici cartesiane di are minima. Rend. Sem. Mat. Fis. Milano, t. 40, 1970, p. 135-153. Zbl0219.53008MR291963
  4. [G2] E. Giusti, Boundary behaviour of non-parametric minimal surfaces. Indiana Univ. Math. J., t. 22, 1972, p. 435-444. Zbl0262.35020MR305253
  5. [G3] E. Giusti, Minimal surfaces and functions of bounded variation. Birkhaüser-Boston Inc. 1984. Zbl0545.49018MR775682
  6. [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. Zbl0159.40204MR222467
  7. [L1] G. Lieberman, The quasilinear Dirichlet problem with decreased regularity at the boundary. Comm. Part. Diff. Equats, t. 6, 1981, p. 437-497. Zbl0458.35039MR612553
  8. [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. Zbl0497.35010MR656797
  9. [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. Zbl0589.35036MR818099
  10. [L0] G. Lorentz, Approximation of functions. Holt, Rinehart and Winston, New York, 1966. Zbl0153.38901MR213785
  11. [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. Zbl0231.35004MR316884
  12. [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. Zbl0295.35027MR352696
  13. [S2] L. Simon, Boundary behaviour of solutions of the nonparametric least area problem. Bull. Austral. Math. Soc., t. 26, 1982, p. 17-27. Zbl0499.49023MR679917
  14. [S3] L. Simon, Personal communication. 
  15. [W1] G. Williams, Solutions of the minimal surface equation continuous and discontinuous at the boundary. Preprint. To appear. Comm. Partial Differential Equations. Zbl0605.49030MR862695
  16. [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. Zbl0541.35033MR767575

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