Under the bounded slope condition on the boundary values of a minimization problem for a functional of the gradient of u, we show that a continuous minimizer w is, in fact, Lipschitzian. An application of this result to prove the validity of the Euler Lagrange equation for w is presented.
Cellina, A. (2001). On the bounded slope condition and the validity of the Euler Lagrange equation. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 40(4), 1270-1279 [10.1137/S0363012999354661].
On the bounded slope condition and the validity of the Euler Lagrange equation
Cellina, A
2001
Abstract
Under the bounded slope condition on the boundary values of a minimization problem for a functional of the gradient of u, we show that a continuous minimizer w is, in fact, Lipschitzian. An application of this result to prove the validity of the Euler Lagrange equation for w is presented.
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