JournalsaihpcVol. 10, No. 4pp. 445–451

On solutions of the exterior Dirichlet problem for the minimal surface equation

  • Ernst Kuwert

    Mathematisches Institut, Universität Bonn, Wegelerstrasse 10, D-53115 Bonn, Germany
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Abstract

Uniqueness and existence results for boundary value problems for the minimal surface equation on exterior domains obtained by Langévin-Rosenberg and Krust in dimension two are generalized to arbitrary dimensions. A suitable n-dimensional version of the maximum principle at infinity is given.

Résumé

On présente des résultats d’unicité et d’existence pour l’équation des surfaces minimales sur un domaine extérieur de ℝn. On donne une généralisation du principe de maximum à l’infini, valable quel que soit n.

Cite this article

Ernst Kuwert, On solutions of the exterior Dirichlet problem for the minimal surface equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), no. 4, pp. 445–451

DOI 10.1016/S0294-1449(16)30211-6