Geodesic
Integrability for vector-valued minimizers of some variational integrals
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 3, pp. 469-479

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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 $p\ge 2$.
Classification : 35J20, 35J60, 49J20, 49J53, 49N60
Keywords: calculus of variations; minimizers; regularity 
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     author = {Leonetti, Francesco and Siepe, Francesco},
     title = {Integrability for vector-valued minimizers of some variational integrals},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {469--479},
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     number = {3},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2001__42_3_a4/}
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Leonetti, Francesco; Siepe, Francesco. Integrability for vector-valued minimizers of some variational integrals. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 3, pp. 469-479. http://geodesic.mathdoc.fr/item/CMUC_2001__42_3_a4/