×

zbMATH — the first resource for mathematics

The Dirichlet Problem for the minimal surface equation on unbounded domains. (Le problème de Dirichlet pour l’équation des surfaces minimales sur des domaines non bornés.) (French) Zbl 0754.53013
On étudie le comportement relatif à l’infinit de deux solutions du problème de Dirichlet pour l’équation des surfaces minimales.
Reviewer: A.Neagu (Iaşi)

MSC:
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
References:
[1] COLLIN (P.) . - Compléments sur les graphes de courbure moyenne constante , à paraître.
[2] GILBARG (D.) and TRUDINGER (N.S.) . - Elliptic partial differential equations of second order , Springer Verlag 1983 . MR 86c:35035 | Zbl 0562.35001 · Zbl 0562.35001
[3] HWANG (J.F.) . - Comparison principles and Liouville theorems for prescribed mean curvature equation in unbounded domains , Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), t. 15, 1988 , p. 341-355. Numdam | MR 90m:35019 | Zbl 0705.49022 · Zbl 0705.49022
[4] JENKINS (H.) and SERRIN (J.) . - Variational problems of minimal surfaces type, II . Boundary value problem for the minimal surface equation, Arch. Rational Mech. Anal., t. 21, 1963 , p. 321-342. Zbl 0171.08301 · Zbl 0171.08301
[5] KRUST (R.) . - Remarques sur le problème extérieur de Plateau , Duke Math. J., t. 59, 1989 , p. 161-173. Article | MR 90i:49050 | Zbl 0709.49022 · Zbl 0709.49022
[6] LANGEVIN (R.) , LEVITT (G.) and ROSENBERG (H.) . - Complete minimal surfaces with long line boundaries , Duke Math. J., t. 55, 4, 1987 , p. 1-11. Article | MR 89h:53022 | Zbl 0637.53007 · Zbl 0637.53007
[7] LANGEVIN (R.) and ROSENBERG (H.) . - A maximal principle at infinity for minimal surfaces and applications , à paraître dans Duke Math., J., t. 57, 1988 , p. 819-828. Article | MR 90c:53025 | Zbl 0667.49024 · Zbl 0667.49024
[8] BLAINE LAWSON (H.) . - Lectures on minimal submanifolds , Vol. 1, Math. Lecture Series 9, Publish or Perish. Zbl 0434.53006 · Zbl 0434.53006
[9] OSSERMAN (R.) . - A survey of minimal surfaces , Van Nostrand Reinhold Math. Studies 25, 1969 . MR 41 #934 | Zbl 0209.52901 · Zbl 0209.52901
[10] PROTTER (M.) and WEINBERGER (H.) . - Maximum principles in differential equations . - Prentice Hall, 1967 . MR 36 #2935 | Zbl 0153.13602 · Zbl 0153.13602
[11] SA EARP (R.) and ROSENBERG (H.) . - The Dirichlet problem for the minimal surface equation on unbounded planar domains , J. Math. Pures Appl., t. 68, 1989 , p. 163-183. MR 90m:35072 | Zbl 0696.49069 · Zbl 0696.49069
[12] SERRIN (J.) . - A priori estimates for solutions of the minimal surface equation , Arch. Rationnal Mech. Anal., t. 14, 1963 , p. 376-383. MR 28 #1386 | Zbl 0117.07304 · Zbl 0117.07304
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.