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We discuss some implications of linear programming for Mather theory [13, 14, 15] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an -dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [6, 7, 8, 5].
@article{COCV_2002__8__693_0,
author = {Evans, L. C. and Gomes, D.},
title = {Linear programming interpretations of {Mather's} variational principle},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {693--702},
publisher = {EDP-Sciences},
volume = {8},
year = {2002},
doi = {10.1051/cocv:2002030},
zbl = {1090.90143},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002030/}
}
TY - JOUR AU - Evans, L. C. AU - Gomes, D. TI - Linear programming interpretations of Mather's variational principle JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2002 SP - 693 EP - 702 VL - 8 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002030/ DO - 10.1051/cocv:2002030 LA - en ID - COCV_2002__8__693_0 ER -
%0 Journal Article %A Evans, L. C. %A Gomes, D. %T Linear programming interpretations of Mather's variational principle %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 693-702 %V 8 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002030/ %R 10.1051/cocv:2002030 %G en %F COCV_2002__8__693_0
Evans, L. C.; Gomes, D. Linear programming interpretations of Mather's variational principle. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 693-702. doi: 10.1051/cocv:2002030
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