# Existence and regularity of minimizers of nonconvex integrals with p-q growth

Pietro Celada; Giovanni Cupini; Marcello Guidorzi

ESAIM: Control, Optimisation and Calculus of Variations (2007)

- Volume: 13, Issue: 2, page 343-358
- ISSN: 1292-8119

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topCelada, Pietro, Cupini, Giovanni, and Guidorzi, Marcello. "Existence and regularity of minimizers of nonconvex integrals with p-q growth." ESAIM: Control, Optimisation and Calculus of Variations 13.2 (2007): 343-358. <http://eudml.org/doc/250001>.

@article{Celada2007,

abstract = {
We show that local minimizers of functionals of the form
$\int_\{\Omega\} \left[f(Du(x)) + g(x\,,u(x))\right]\,\{\rm d\}x$, $u \in u_0 + W_0^\{1,p\}(\Omega)$,
are locally Lipschitz continuous provided f is a convex function with $p-q$ growth
satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous
in u. As a consequence of this, we obtain an existence result for a related nonconvex
functional.
},

author = {Celada, Pietro, Cupini, Giovanni, Guidorzi, Marcello},

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

keywords = {Nonstandard growth; existence; Lipschitz continuity; Non standard growth},

language = {eng},

month = {5},

number = {2},

pages = {343-358},

publisher = {EDP Sciences},

title = {Existence and regularity of minimizers of nonconvex integrals with p-q growth},

url = {http://eudml.org/doc/250001},

volume = {13},

year = {2007},

}

TY - JOUR

AU - Celada, Pietro

AU - Cupini, Giovanni

AU - Guidorzi, Marcello

TI - Existence and regularity of minimizers of nonconvex integrals with p-q growth

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2007/5//

PB - EDP Sciences

VL - 13

IS - 2

SP - 343

EP - 358

AB -
We show that local minimizers of functionals of the form
$\int_{\Omega} \left[f(Du(x)) + g(x\,,u(x))\right]\,{\rm d}x$, $u \in u_0 + W_0^{1,p}(\Omega)$,
are locally Lipschitz continuous provided f is a convex function with $p-q$ growth
satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous
in u. As a consequence of this, we obtain an existence result for a related nonconvex
functional.

LA - eng

KW - Nonstandard growth; existence; Lipschitz continuity; Non standard growth

UR - http://eudml.org/doc/250001

ER -

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