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Keywords:
calculus of variations; minimizers; regularity
calculus of variations; minimizers; regularity
Summary:
We prove that the higher integrability of the data $f, f_0$ improves on the integrability of minimizers $u$ of functionals $\Cal F$, whose model is $$ \int_{\Omega} \left[|Du|^p + (\operatorname{det} (Du))^2 - \langle f,Du \rangle + \langle f_0,u \rangle \right] dx, $$ where $u:\Omega\subset \Bbb R^n\to \Bbb R^n$ and $p\ge 2$.
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