A finite dimensional linear programming approximation of Mather's variational problem

Luca Granieri

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

  • Volume: 16, Issue: 4, page 1094-1109
  • ISSN: 1292-8119

Abstract

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We provide an approximation of Mather variational problem by finite dimensional minimization problems in the framework of Γ-convergence. By a linear programming interpretation as done in [Evans and Gomes, ESAIM: COCV 8 (2002) 693–702] we state a duality theorem for the Mather problem, as well a finite dimensional approximation for the dual problem.

How to cite

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Granieri, Luca. "A finite dimensional linear programming approximation of Mather's variational problem." ESAIM: Control, Optimisation and Calculus of Variations 16.4 (2010): 1094-1109. <http://eudml.org/doc/250754>.

@article{Granieri2010,
abstract = { We provide an approximation of Mather variational problem by finite dimensional minimization problems in the framework of Γ-convergence. By a linear programming interpretation as done in [Evans and Gomes, ESAIM: COCV 8 (2002) 693–702] we state a duality theorem for the Mather problem, as well a finite dimensional approximation for the dual problem. },
author = {Granieri, Luca},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Mather problem; minimal measures; linear programming; Γ-convergence; -convergence},
language = {eng},
month = {10},
number = {4},
pages = {1094-1109},
publisher = {EDP Sciences},
title = {A finite dimensional linear programming approximation of Mather's variational problem},
url = {http://eudml.org/doc/250754},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Granieri, Luca
TI - A finite dimensional linear programming approximation of Mather's variational problem
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/10//
PB - EDP Sciences
VL - 16
IS - 4
SP - 1094
EP - 1109
AB - We provide an approximation of Mather variational problem by finite dimensional minimization problems in the framework of Γ-convergence. By a linear programming interpretation as done in [Evans and Gomes, ESAIM: COCV 8 (2002) 693–702] we state a duality theorem for the Mather problem, as well a finite dimensional approximation for the dual problem.
LA - eng
KW - Mather problem; minimal measures; linear programming; Γ-convergence; -convergence
UR - http://eudml.org/doc/250754
ER -

References

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  15. J. Jost, Riemannian Geometry and Geometric Analysis. Springer (2002).  
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