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

Abstract

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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.

How to cite

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Fonseca, 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 -

References

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