# Integral representation and Γ-convergence of variational integrals with p(x)-growth

Alessandra Coscia; Domenico Mucci

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

- Volume: 7, page 495-519
- ISSN: 1292-8119

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topCoscia, Alessandra, and Mucci, Domenico. "Integral representation and Γ-convergence of variational integrals with p(x)-growth." ESAIM: Control, Optimisation and Calculus of Variations 7 (2010): 495-519. <http://eudml.org/doc/90633>.

@article{Coscia2010,

abstract = {
We study the integral representation properties of limits of sequences of
integral functionals like $\int f(x,Du)\,\{\rm d\}x$ under
nonstandard growth conditions of (p,q)-type: namely, we assume that
$$
\vert z\vert^\{p(x)\}\leq f(x,z)\leq L(1+\vert z\vert^\{p(x)\})\,.
$$
Under weak assumptions on the continuous function p(x), we prove
Γ-convergence to integral functionals of the same type.
We also analyse the case of integrands f(x,u,Du) depending explicitly
on u; finally we weaken the assumption allowing p(x) to be
discontinuous on nice sets.
},

author = {Coscia, Alessandra, Mucci, Domenico},

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

keywords = {Integral representation; Γ-convergence; nonstandard
growth conditions.; integral representation; Gamma-convergence; nonstandard growth conditions; integral functionals},

language = {eng},

month = {3},

pages = {495-519},

publisher = {EDP Sciences},

title = {Integral representation and Γ-convergence of variational integrals with p(x)-growth},

url = {http://eudml.org/doc/90633},

volume = {7},

year = {2010},

}

TY - JOUR

AU - Coscia, Alessandra

AU - Mucci, Domenico

TI - Integral representation and Γ-convergence of variational integrals with p(x)-growth

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 7

SP - 495

EP - 519

AB -
We study the integral representation properties of limits of sequences of
integral functionals like $\int f(x,Du)\,{\rm d}x$ under
nonstandard growth conditions of (p,q)-type: namely, we assume that
$$
\vert z\vert^{p(x)}\leq f(x,z)\leq L(1+\vert z\vert^{p(x)})\,.
$$
Under weak assumptions on the continuous function p(x), we prove
Γ-convergence to integral functionals of the same type.
We also analyse the case of integrands f(x,u,Du) depending explicitly
on u; finally we weaken the assumption allowing p(x) to be
discontinuous on nice sets.

LA - eng

KW - Integral representation; Γ-convergence; nonstandard
growth conditions.; integral representation; Gamma-convergence; nonstandard growth conditions; integral functionals

UR - http://eudml.org/doc/90633

ER -

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