Everywhere regularity for vectorial functionals with general growth
ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003), pp. 399-418.

We prove Lipschitz continuity for local minimizers of integral functionals of the Calculus of Variations in the vectorial case, where the energy density depends explicitly on the space variables and has general growth with respect to the gradient. One of the models is

 $F\left(u\right)={\int }_{\Omega }a\left(x\right){\left[h\left(|Du|\right)\right]}^{p\left(x\right)}\mathrm{d}x$
with $h$ a convex function with general growth (also exponential behaviour is allowed).

DOI: 10.1051/cocv:2003019
Classification: 49N60,  35J50
Keywords: minimizers, regularity, nonstandard growth, exponential growth
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Mascolo, Elvira; Migliorini, Anna Paola. Everywhere regularity for vectorial functionals with general growth. ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003), pp. 399-418. doi : 10.1051/cocv:2003019. http://www.numdam.org/articles/10.1051/cocv:2003019/

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