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Partial regularity for anisotropic functionals of higher order. (English) Zbl 1130.35317

Summary: We prove a \(C^{k,\alpha}\) partial regularity result for local minimizers of variational integrals of the type \(I(u)=\int_\Omega f(D^{k}u(x))\,dx\), assuming that the integrand \(f\) satisfies (\(p,q)\) growth conditions.

MSC:

35D10 Regularity of generalized solutions of PDE (MSC2000)
49N60 Regularity of solutions in optimal control
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