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higher order derivatives

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Partial regularity for anisotropic functionals of higher order
Menita Carozza, Antonia Passarelli di Napoli
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 13 / Issue 4 / October 2007

Published online by Cambridge University Press:

20 July 2007, pp. 692-706

Print publication:

October 2007
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 We prove a $C^{k,\alpha}$ partial regularity result for local minimizers of variationalintegrals of the type $I(u)=\int_\Omega f(D^{k}u(x)){\rm d}x$ , assumingthat the integrand f satisfies (p,q) growth conditions.