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

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

Keywords: minimizers, regularity, nonstandard growth, exponential growth

@article{COCV_2003__9__399_0, author = {Mascolo, Elvira and Migliorini, Anna Paola}, title = {Everywhere regularity for vectorial functionals with general growth}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {399--418}, publisher = {EDP-Sciences}, volume = {9}, year = {2003}, doi = {10.1051/cocv:2003019}, zbl = {1066.49023}, mrnumber = {1988669}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2003019/} }

TY - JOUR AU - Mascolo, Elvira AU - Migliorini, Anna Paola TI - Everywhere regularity for vectorial functionals with general growth JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2003 DA - 2003/// SP - 399 EP - 418 VL - 9 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2003019/ UR - https://zbmath.org/?q=an%3A1066.49023 UR - https://www.ams.org/mathscinet-getitem?mr=1988669 UR - https://doi.org/10.1051/cocv:2003019 DO - 10.1051/cocv:2003019 LA - en ID - COCV_2003__9__399_0 ER -

%0 Journal Article %A Mascolo, Elvira %A Migliorini, Anna Paola %T Everywhere regularity for vectorial functionals with general growth %J ESAIM: Control, Optimisation and Calculus of Variations %D 2003 %P 399-418 %V 9 %I EDP-Sciences %U https://doi.org/10.1051/cocv:2003019 %R 10.1051/cocv:2003019 %G en %F COCV_2003__9__399_0

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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