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The best modulus of continuity for solutions of the minimal surface equation

Journal Article


Abstract


  • We consider the Dirichlet problem for the minimal surface equation on a bounded domain in Rn which has nonnegative mean curvature. We give a modulus of continuity for the solution u in terms of the modulus of continuity of the boundary values φ. The modulus obtained is shown to be best possible. © 1987 by Pacific Journal of Mathematics.

Publication Date


  • 1987

Citation


  • Williams, G. H. (1987). The best modulus of continuity for solutions of the minimal surface equation. Pacific Journal of Mathematics, 129(1), 193-208. doi:10.2140/pjm.1987.129.193

Scopus Eid


  • 2-s2.0-84972580108

Web Of Science Accession Number


Start Page


  • 193

End Page


  • 208

Volume


  • 129

Issue


  • 1

Abstract


  • We consider the Dirichlet problem for the minimal surface equation on a bounded domain in Rn which has nonnegative mean curvature. We give a modulus of continuity for the solution u in terms of the modulus of continuity of the boundary values φ. The modulus obtained is shown to be best possible. © 1987 by Pacific Journal of Mathematics.

Publication Date


  • 1987

Citation


  • Williams, G. H. (1987). The best modulus of continuity for solutions of the minimal surface equation. Pacific Journal of Mathematics, 129(1), 193-208. doi:10.2140/pjm.1987.129.193

Scopus Eid


  • 2-s2.0-84972580108

Web Of Science Accession Number


Start Page


  • 193

End Page


  • 208

Volume


  • 129

Issue


  • 1