Everywhere regularity for vectorial functionals with general growth

Elvira Mascolo; Anna Paola Migliorini

ESAIM: Control, Optimisation and Calculus of Variations (2010)

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

Abstract

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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 u = Ω a ( x ) [ h | D u | ] p ( x ) d x with h a convex function with general growth (also exponential behaviour is allowed).

How to cite

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Mascolo, Elvira, and Migliorini, Anna Paola. "Everywhere regularity for vectorial functionals with general growth." ESAIM: Control, Optimisation and Calculus of Variations 9 (2010): 399-418. <http://eudml.org/doc/90702>.

@article{Mascolo2010,
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.; minimizers; exponential growth},
language = {eng},
month = {3},
pages = {399-418},
publisher = {EDP Sciences},
title = {Everywhere regularity for vectorial functionals with general growth},
url = {http://eudml.org/doc/90702},
volume = {9},
year = {2010},
}

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
DA - 2010/3//
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.; minimizers; exponential growth
UR - http://eudml.org/doc/90702
ER -

References

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