Displaying similar documents to “Monotonicity properties of minimizers and relaxation for autonomous variational problems”

Monotonicity properties of minimizers and relaxation for autonomous variational problems

Giovanni Cupini, Cristina Marcelli (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the following classical autonomous variational problem minimize F ( v ) = ∫ a b f ( v ( x ) , v ' ( x ) ) x ̣ : v ∈ A C ( [ a , b ] ) , v ( a ) = α , v ( b ) = β , where the Lagrangian f is possibly neither continuous, nor convex, nor coercive. We prove a monotonicity property of the minimizers stating that they satisfy the maximum principle or the minimum one. By virtue of such a property, applying recent results concerning constrained variational problems, we derive a relaxation theorem, the DuBois-Reymond...

A note on Minty type vector variational inequalities

Giovanni P. Crespi, Ivan Ginchev, Matteo Rocca (2006)

RAIRO - Operations Research

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The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space ...