Displaying similar documents to “Existence of minimizers of free autonomous variational problems via solvability of constrained ones”

Existence and regularity of minimizers of nonconvex integrals with growth

Pietro Celada, Giovanni Cupini, Marcello Guidorzi (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We show that local minimizers of functionals of the form ∫ Ω f ( D u ( x ) ) + g ( x , u ( x ) ) d x ,  u ∈ u 0 + W 0 1 , p ( Ω ) , are locally Lipschitz continuous provided is a convex function with p - q growth satisfying a condition of qualified convexity at infinity and is Lipschitz continuous in . As a consequence of this, we obtain an existence result for a related nonconvex functional.

Non-local approximation of free-discontinuity problems with linear growth

Luca Lussardi, Enrico Vitali (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We approximate, in the sense of -convergence, free-discontinuity functionals with linear growth in the gradient by a sequence of non-local integral functionals depending on the average of the gradients on small balls. The result extends to higher dimension what we already proved in the one-dimensional case.

Abstract variational problems with volume constraints

Marc Oliver Rieger (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.