A Haar-Rado type theorem for minimizers in Sobolev spaces
Dipartimento di Matematica Pura ed Applicata – Università Degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy.
Let be a minimum for
where f is convex, is convex for a.e. x. We prove that u shares the same modulus of continuity of ϕ whenever Ω is sufficiently regular, the right derivative of g satisfies a suitable monotonicity assumption and the following inequality holds
This result generalizes the classical Haar-Rado theorem for Lipschitz functions.
Mathematics Subject Classification: 49K20
Key words: Hölder / regularity / Lipschitz
© EDP Sciences, SMAI, 2010