Displaying similar documents to “ Γ -convergence and absolute minimizers for supremal functionals”

On lower semicontinuity in the calculus of variations

Giovanni Leoni (2001)

Bollettino dell'Unione Matematica Italiana

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Vengono studiate proprietà di semicontinuità per integrali multipli u ∈ W k , 1 ⁢ Ω ; R d ↦ ∫ Ω f ⁢ x , u ⁢ x , … ⁢ ∇ k ⁡ u ⁢ x ⁢ d ⁢ x quando f soddisfa a condizioni di semicontinuità nelle variabili x , u , … , ∇ k - 1 ⁡ u ⁢ x e può non essere soggetta a ipotesi di coercitività, e le successioni ammissibili in W k , 1 ⁢ Ω ; R d convergono fortemente in W k - 1 , 1 ⁢ Ω ; R d .

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.