Adjoint methods for obstacle problems and weakly coupled systems of PDE

Filippo Cagnetti; Diogo Gomes; Hung Vinh Tran

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 3, page 754-779
  • ISSN: 1292-8119

Abstract

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The adjoint method, recently introduced by Evans, is used to study obstacle problems, weakly coupled systems, cell problems for weakly coupled systems of Hamilton − Jacobi equations, and weakly coupled systems of obstacle type. In particular, new results about the speed of convergence of some approximation procedures are derived.

How to cite

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Cagnetti, Filippo, Gomes, Diogo, and Tran, Hung Vinh. "Adjoint methods for obstacle problems and weakly coupled systems of PDE." ESAIM: Control, Optimisation and Calculus of Variations 19.3 (2013): 754-779. <http://eudml.org/doc/272901>.

@article{Cagnetti2013,
abstract = {The adjoint method, recently introduced by Evans, is used to study obstacle problems, weakly coupled systems, cell problems for weakly coupled systems of Hamilton − Jacobi equations, and weakly coupled systems of obstacle type. In particular, new results about the speed of convergence of some approximation procedures are derived.},
author = {Cagnetti, Filippo, Gomes, Diogo, Tran, Hung Vinh},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {adjoint methods; cell problems; Hamilton − Jacobi equations; obstacle problems; weakly coupled systems; weak KAM theory},
language = {eng},
number = {3},
pages = {754-779},
publisher = {EDP-Sciences},
title = {Adjoint methods for obstacle problems and weakly coupled systems of PDE},
url = {http://eudml.org/doc/272901},
volume = {19},
year = {2013},
}

TY - JOUR
AU - Cagnetti, Filippo
AU - Gomes, Diogo
AU - Tran, Hung Vinh
TI - Adjoint methods for obstacle problems and weakly coupled systems of PDE
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2013
PB - EDP-Sciences
VL - 19
IS - 3
SP - 754
EP - 779
AB - The adjoint method, recently introduced by Evans, is used to study obstacle problems, weakly coupled systems, cell problems for weakly coupled systems of Hamilton − Jacobi equations, and weakly coupled systems of obstacle type. In particular, new results about the speed of convergence of some approximation procedures are derived.
LA - eng
KW - adjoint methods; cell problems; Hamilton − Jacobi equations; obstacle problems; weakly coupled systems; weak KAM theory
UR - http://eudml.org/doc/272901
ER -

References

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  9. [9] D.A. Gomes, A stochastic analogue of Aubry-Mather theory. Nonlinearity15 (2002) 581–603. Zbl1073.37078MR1901094
  10. [10] H. Ishii and S. Koike, Viscosity solutions for monotone systems of second-order elliptic PDEs. Commun. Partial Differ. Equ.16 (1991) 1095–1128. Zbl0742.35022MR1116855
  11. [11] K. Ishii and N. Yamada, On the rate of convergence of solutions for the singular perturbations of gradient obstacle problems. Funkcial. Ekvac.33 (1990) 551–562. Zbl0728.35006MR1086777
  12. [12] P.L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics. Pitman (Advanced Publishing Program), Boston, Mass. 69 (1982). Zbl0497.35001MR667669
  13. [13] P.L. Lions, G. Papanicolaou and S.R.S. Varadhan, Homogenization of Hamilton-Jacobi equations, Preliminary Version, (1988). 
  14. [14] H.V. Tran, Adjoint methods for static Hamilton-Jacobi equations. Calc. Var. Partial Differ. Equ.41 (2011) 301–319. Zbl1231.35043MR2796233

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