We consider a functional I(u) = integral(Omega)f(del(x)) dx on u(0) + W(1,1)(Omega). Under the assumption that f is just convex, we prove a new Comparison Principle, we improve and give a short proof of Cellina's Comparison result for a new class of minimizers. We then extend a local Lipschitz regularity result obtained recently by Clarke for a wider class of functions f and boundary data u(0) satisfying a new one-sided Bounded Slope Condition. A relaxation result follows.
Local Lipschitz Regularity of Minima For A Scalar Problem of the Calculus of Variations
MARICONDA, CARLO;TREU, GIULIA
2008
Abstract
We consider a functional I(u) = integral(Omega)f(del(x)) dx on u(0) + W(1,1)(Omega). Under the assumption that f is just convex, we prove a new Comparison Principle, we improve and give a short proof of Cellina's Comparison result for a new class of minimizers. We then extend a local Lipschitz regularity result obtained recently by Clarke for a wider class of functions f and boundary data u(0) satisfying a new one-sided Bounded Slope Condition. A relaxation result follows.
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