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A \({C^{1,\alpha}}\) partial regularity result for non-autonomous convex integrals with discontinuous coefficients

  • Antonia Passarelli di NapoliEmail author
Article

Abstract

We establish the \({C^{1,\alpha}}\) partial regularity of vectorial minimizers of non autonomous convex integral functionals of the type
$$\mathcal{F}(u;\,\Omega):=\int_{\Omega}f(x, Du)\, dx,$$
with p-growth into the gradient variable. As a novel feature, we allow discontinuous dependence on the x variable, through a suitable Sobolev function. The Hölder’s continuity of the gradient of the minimizers is obtained outside a negligible set and this an unavoidable feature in the vectorial setting. Here, the so called singular set has to take into account also of the possible discontinuity of the coefficients.

Mathematics Subject Classification

Primary 49N15 49N60 Secondary 49N99 

Keywords

Variational integrals Discontinuous coefficients Partial regularity 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Applicazioni “R. Caccioppoli”Università di Napoli “Federico II”NapoliItaly

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