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Regularity of minima of variational integrals. (English) Zbl 0961.49022
The paper deals with the regularity of derivatives of functions $$u$$ minimizing the variational integral $$F(u,\Omega)=\int_\Omega f(x,u,Du) dx$$, where $$\Omega \subset \mathbb R^n$$, $$n>1$$, is an open set, $$u: \Omega \to \mathbb R^N$$, $$N>1$$, $$Du=\{D_\alpha u^i\}$$, $$\alpha =1,\dots ,n$$, $$i=1,\dots ,N$$ and $$f: \Omega \times \mathbb R^N\times \mathbb R^{nN}\to \mathbb R$$ satisfies certain conditions such that either $$Du\in L_{\text{loc}}^{2,n(1-1/p)}(\Omega ,\mathbb R^{nN})$$ or $$Du\in \mathcal L^{2,n}_{\text{loc}}(\Omega ,\mathbb R^{nN})$$ for some $$p>1$$.

##### MSC:
 49N60 Regularity of solutions in optimal control 35J60 Nonlinear elliptic equations
##### Keywords:
nonlinear functional; regularity; Campanato-Morrey spaces
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##### References:
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