Displaying similar documents to “Variational problems with lipschitzian minimizers”

Continuity of solutions to a basic problem in the calculus of variations

Francis Clarke (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study the problem of minimizing ∫ Ω F ( D u ( x ) ) d x over the functions u ∈ W 1 , 1 ( Ω ) that assume given boundary values φ on Γ : = ∂ Ω . The lagrangian F and the domain Ω are assumed convex. A new type of hypothesis on the boundary function φ is introduced: the (or upper) . This condition, which is less restrictive than the familiar bounded slope condition of Hartman, Nirenberg and Stampacchia, allows us to extend the classical Hilbert-Haar regularity theory to the case of semiconvex (or semiconcave) boundary data (instead...