# Everywhere regularity for vectorial functionals with general growth

Elvira Mascolo; Anna Paola Migliorini

ESAIM: Control, Optimisation and Calculus of Variations (2003)

- Volume: 9, page 399-418
- ISSN: 1292-8119

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topMascolo, Elvira, and Migliorini, Anna Paola. "Everywhere regularity for vectorial functionals with general growth." ESAIM: Control, Optimisation and Calculus of Variations 9 (2003): 399-418. <http://eudml.org/doc/244758>.

@article{Mascolo2003,

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

author = {Mascolo, Elvira, Migliorini, Anna Paola},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {minimizers; regularity; nonstandard growth; exponential growth},

language = {eng},

pages = {399-418},

publisher = {EDP-Sciences},

title = {Everywhere regularity for vectorial functionals with general growth},

url = {http://eudml.org/doc/244758},

volume = {9},

year = {2003},

}

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

PB - EDP-Sciences

VL - 9

SP - 399

EP - 418

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

LA - eng

KW - minimizers; regularity; nonstandard growth; exponential growth

UR - http://eudml.org/doc/244758

ER -

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