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 over the functions that assume given boundary values on . The lagrangian and the domain are assumed convex. A new type of hypothesis on the boundary function 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...