# An existence result for a nonconvex variational problem via regularity

Irene Fonseca; Nicola Fusco^{[1]}; Paolo Marcellini

- [1] Dipartimento di Matematica e Applicazioni Monte Sant’Angelo, via Cintia, 80126 Napoli, Italy;

ESAIM: Control, Optimisation and Calculus of Variations (2002)

- Volume: 7, page 69-95
- ISSN: 1292-8119

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topFonseca, Irene, Fusco, Nicola, and Marcellini, Paolo. "An existence result for a nonconvex variational problem via regularity." ESAIM: Control, Optimisation and Calculus of Variations 7 (2002): 69-95. <http://eudml.org/doc/244986>.

@article{Fonseca2002,

abstract = {Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The $x$-dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.},

affiliation = {Dipartimento di Matematica e Applicazioni Monte Sant’Angelo, via Cintia, 80126 Napoli, Italy;},

author = {Fonseca, Irene, Fusco, Nicola, Marcellini, Paolo},

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

keywords = {nonconvex variational problems; uniform convexity; regularity; implicit differential equations; variational problems; nonconvex integrands; existence of minimizers},

language = {eng},

pages = {69-95},

publisher = {EDP-Sciences},

title = {An existence result for a nonconvex variational problem via regularity},

url = {http://eudml.org/doc/244986},

volume = {7},

year = {2002},

}

TY - JOUR

AU - Fonseca, Irene

AU - Fusco, Nicola

AU - Marcellini, Paolo

TI - An existence result for a nonconvex variational problem via regularity

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2002

PB - EDP-Sciences

VL - 7

SP - 69

EP - 95

AB - Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The $x$-dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.

LA - eng

KW - nonconvex variational problems; uniform convexity; regularity; implicit differential equations; variational problems; nonconvex integrands; existence of minimizers

UR - http://eudml.org/doc/244986

ER -

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## Citations in EuDML Documents

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- Pietro Celada, Giovanni Cupini, Marcello Guidorzi, Existence and regularity of minimizers of nonconvex integrals with growth
- Bruno De Maria, A regularity result for a convex functional and bounds for the singular set
- Michela Eleuteri, Hölder continuity results for a class of functionals with non-standard growth
- Giuseppe Mingione, Regularity of minima: an invitation to the Dark Side of the Calculus of Variations

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