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

Abstract

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We show that local minimizers of functionals of the form ∫ Ω f ( D u ( x ) ) + g ( x , u ( x ) ) d x ,  u ∈ u 0 + W 0 1 , p ( Ω ) , 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.

How to cite

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Celada, 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 -

References

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