Everywhere regularity for vectorial functionals with general growth

Mascolo, Elvira; Migliorini, Anna Paola

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

$$F\left(u\right)={\int }_{\Omega }a\left(x\right){\left[h\left(\left|Du\right|\right)\right]}^{p\left(x\right)}\mathrm{d}x$$

with $h$ a convex function with general growth (also exponential behaviour is allowed).

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