Adjoint methods for obstacle problems and weakly coupled systems of PDE

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 19, Issue 3, 2013, Pages 754-779

  Cagnetti, Filippo ^a   Gomes, Diogo ^a   Tran, Hung Vinh ^b  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Adjoint methods; Cell problems; Hamilton Jacobi equations; Obstacle problems; Weak KAM theory; Weakly coupled systems

Indexed keywords

ADJOINT METHODS; CELL PROBLEMS; HAMILTON - JACOBI EQUATIONS; KAM THEORY; OBSTACLE PROBLEMS; WEAKLY COUPLED SYSTEMS;

CONTROL;

MECHANICS;

EID: 84881110499     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv/2012032     Document Type: Article

References (14)

1. G. Barles and B. Perthame, Exit time problems in optimal control and vanishing viscosity method. SIAM J. Control Optim. 26 (1988) 1133-1148.
2. I. Capuzzo-Dolcetta and L.C. Evans, Optimal switching for ordinary differential equations. SIAM J. Control Optim. 22 (1984) 143-161.
3. F. Cagnetti, D. Gomes and H.V. Tran, Aubry-Mather measures in the nonconvex setting. SIAM J. Math. Anal. 43 (2011) 2601-2629.
4. F. Camilli and P. Loreti, Comparison results for a class of weakly coupled systems of eikonal equations. Hokkaido Math. J. 37 (2008) 349-362.
5. F. Camilli, P. Loreti, and N. Yamada, Systems of convex Hamilton-Jacobi equations with implicit obstacles and the obstacle problem. Commun. Pure Appl. Anal. 8 (2009) 1291-1302.
6. H. Engler and S.M. Lenhart, Viscosity solutions for weakly coupled systems of Hamilton-Jacobi equations. Proc. London Math. Soc. 63 (1991) 212-240.
7. L.C. Evans and C.K. Smart, Adjoint methods for the infinity Laplacian partial differential equation. Arch. Ration. Mech. Anal. 201 (2011) 87-113.
8. L.C. Evans, Adjoint and compensated compactness methods for Hamilton-Jacobi PDE. Arch. Ration. Mech. Anal. 197 (2010) 1053-1088.
9. D.A. Gomes, A stochastic analogue of Aubry-Mather theory. Nonlinearity 15 (2002) 581-603.
10. H. Ishii and S. Koike, Viscosity solutions for monotone systems of second-order elliptic PDEs. Commun. Partial Differ. Equ. 16 (1991) 1095-1128.
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.
12. P.L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics. Pitman (Advanced Publishing Program), Boston, Mass. 69 (1982).
13. P.L. Lions, G. Papanicolaou and S.R.S. Varadhan, Homogenization of Hamilton-Jacobi equations, Preliminary Version, (1988).
14. H.V. Tran, Adjoint methods for static Hamilton-Jacobi equations. Calc. Var. Partial Differ. Equ. 41 (2011) 301-319.