ON TWO DIMENSIONAL VARIATIONAL PROBLEMS IN PARAMETRIC FORM

Abstract

The geometrical relationships between a closed surface and a solution surface are studied. The mapping of a solution surface S, into a closed surface in the case of regular variational problems gives rise to a canonical mapping of S onto the solution of a non-parametric, uniformly elliptic variational problem. The principal application is to show that solutions of some variational problems behave qualitatively like minimal surfaces, in the same sense that solutions of uniformly elliptic equations behave like solutions of the Laplace equation. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 15, 1961
Accession Number
AD0259147

Entities

People

  • H.b. Jenkins

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Equations
  • Geometry
  • Mathematics
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Operations Research
  • Statistical inference.