Abstract

This paper studies the solutions of the minimum problem for a functional of the gradient under linear boundary conditions. A necessary and sufficient condition, based on the facial structure of the epigraph of the integrand, is provided for the continuous dependence of the solutions on boundary data.

MSC codes

  1. 49A50

Keywords

  1. calculus of variations
  2. extrema.lity
  3. strong convergence
  4. weak convergence

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References

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Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 1114 - 1127
ISSN (online): 1095-7138

History

Submitted: 20 July 1992
Accepted: 22 January 1993
Published online: 1 August 2006

MSC codes

  1. 49A50

Keywords

  1. calculus of variations
  2. extrema.lity
  3. strong convergence
  4. weak convergence

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