JournalsrlmVol. 26, No. 4pp. 475–496

Regularity results for non-autonomous variational integrals with discontinuous coefficients

  • Antonia Passarelli di Napoli

    Università degli Studi di Napoli Federico II, Italy
Regularity results for non-autonomous variational integrals with discontinuous coefficients cover
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Abstract

We investigate the regularity propertiesof local minimizers of non autonomous convex integral functionals of the type

F(u;Ω):=Ωf(x,Du) dx,\mathcal{F}(u; \Omega):= \int_{\Omega} f (x, Du) \ dx ,

with pp-growth into the gradient variable and discontinuous dependence on the xx variable. We prove a higher differentiability result for local minimizers of the functional F(u;Ω)\mathcal{F}(u; \Omega) assuming that the function that measures the oscillation of the integrand with respect to the xx variable belongs to a suitable Sobolev space.

Cite this article

Antonia Passarelli di Napoli, Regularity results for non-autonomous variational integrals with discontinuous coefficients. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 4, pp. 475–496

DOI 10.4171/RLM/717