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We study two-point Lagrange problems for integrands L = L(t; u;v): F (u )= Z b a L (t; u(t); _ u(t)) dt ! inf; u 2A = f v 2 W 1 ; 1((a; b);Rn)jv(a )= A;v(b )= B g : (P)

A condition on the value function both necessary and sufficient for full regularity of minimizers of one-dimensional variational problems