Francesco Leonetti, Francesco Siepe
Integrability for vector-valued minimizers of somevariational integrals

Comment.Math.Univ.Carolinae42,3 (2001) 469-479.

Abstract:We prove that thehigher integrability of the data $f, f_0$ improves on theintegrability of minimizers $u$ of functionals $\Cal F$, whosemodel is $$ \int _{\Omega } \left [|Du|^p + (det (Du))^2 -\langle f,Du \rangle + \langle f_0,u \rangle \right ] dx, $$ where $u:\Omega \subset \Bbb R^n\to \Bbb R^n$ and $p\ge 2$.

Keywords: calculus of variations, minimizers, regularity
AMS Subject Classification: 49N60, 35J60