SIAM Journal on Control and Optimization, Vol.32, No.4, 1114-1127, 1994
A Version of Olechs Lemma in a Problem of the Calculus of Variations
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.