# An existence result for a nonconvex variational problem via regularity

Irene Fonseca; Nicola Fusco; Paolo Marcellini

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

- 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 (2010): 69-95. <http://eudml.org/doc/90637>.

@article{Fonseca2010,

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.
},

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},

month = {3},

pages = {69-95},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/90637},

volume = {7},

year = {2010},

}

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

DA - 2010/3//

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/90637

ER -

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