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.
Cellina, A., Zagatti, S. (1994). A version of Olech's lemma in a problem of the calculus of variations. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 32(4), 1114-1127 [10.1137/S0363012992234669].
A version of Olech's lemma in a problem of the calculus of variations
CELLINA, ARRIGO;
1994
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.
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