Free Access
Volume 21, Number 4, October-December 2015
Page(s) 1108 - 1119
Published online 24 June 2015
  1. G. Alberti, Variational models for phase transitions, an approach via Γ-convergence. Calc. Var. Partial Differ. Equ. Edited by G. Buttazzo, A. Marino and M.K.V. Murthy. Springer, Berlin, Heidelberg (2000) 95–114. [Google Scholar]
  2. Z. Artsein and I. Bright, Periodic optimization suffices for infinite horizon planar optimal control. SIAM J. Control Optim. 48 (2010) 4963–4986. [CrossRef] [MathSciNet] [Google Scholar]
  3. Z. Artstein and A. Leizarowitz, Singularly perturbed control systems with one-dimensional fast dynamics. SIAM J. Control Optim. 41 (2002) 641–658. [CrossRef] [MathSciNet] [Google Scholar]
  4. P. Billingsley, Convergence of probability Measures. Wiley, New York (1968). [Google Scholar]
  5. A. Braides, A handbook of Γ-convergence. Vol. 3 of Stationary Partial Differential Equations. Edited by M. Chipot and P. Quittner. North-Holland (2006) 101–213. [Google Scholar]
  6. I. Bright, A reduction of topological infinite-horizon optimization to periodic optimization in a class of compact 2-manifolds. J. Math. Anal. Appl. 394 (2012) 84–101. [CrossRef] [MathSciNet] [Google Scholar]
  7. J.W. Cahn and J.E. Hilliard, Free energy of a nonuniform system. i. interfacial free energy. J. Chem. Phys. 28 (1958) 258–267. [CrossRef] [Google Scholar]
  8. J. Carr, M.E. Gurtin and M. Slemrod, Structured phase transitions on a finite interval. Arch. Ration. Mech. Anal. 86 (1984) 317–351. [CrossRef] [Google Scholar]
  9. J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian. Probl. Anal. 625 (1970) 195–199. [Google Scholar]
  10. K. Ciesielski, On the Poincaré–Bendixson theorem. Lect. Notes Nonlin. Anal. 3 (2002) 49–69. [Google Scholar]
  11. K. Ciesielski, The Poincaré–Bendixson Theorem: from Poincaré to the XXIst century. Cent. Eur. J. Math. 10 (2012) 2110–2128. [CrossRef] [MathSciNet] [Google Scholar]
  12. F. Colonius and M. Sieveking, Asymptotic properties of optimal solutions in planar discounted control problems. SIAM J. Control Optim. 27 (1989) 608. [CrossRef] [MathSciNet] [Google Scholar]
  13. V. Gaitsgory and S. Rossomakhine, Linear programming approach to deterministic long run average problems of optimal control. SIAM J. Control Optim. 44 (2006) 2006–2037. [CrossRef] [MathSciNet] [Google Scholar]
  14. V. Gaitsgory, S. Rossomakhine and N. Thatcher, Approximate solution of the HJB inequality related to the infinite horizon optimal control problem with discounting. Dynam. of Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 19 (2012) 65–92. [Google Scholar]
  15. I.R. Ionescu and T. Lachand–Robert, Generalized Cheeger sets related to landslides. Calc. Var. Partial Differ. Equ. 23 (2005) 227–249. [Google Scholar]
  16. B. Kawohl and T. Lachand–Robert, Characterization of Cheeger sets for convex subsets of the plane. Pacific J. Math. 225 (2006) 103–118. [Google Scholar]
  17. A. Leizarowitz and V.J. Mizel, One dimensional infinite-horizon variational problems arising in continuum mechanics. Arch. Ration. Mech. Anal. 106 (1989) 161–194. [CrossRef] [MathSciNet] [Google Scholar]
  18. L. Modica and S. Mortola, Un esempio di Γ-convergenza. Boll. Un. Mat. It. B 14 (1977) 285–299. [Google Scholar]
  19. J.S. Rowlinson, Translation of J.D. van der Waals: The thermodynamik theory of capillarity under the hypothesis of a continuous variation of density. J. Stat. Phys. 20 (1979) 197–200. [CrossRef] [MathSciNet] [Google Scholar]
  20. P. Sternberg, The effect of a singular perturbation on nonconvex variational problems. Arch. Ration. Mech. Anal. 101 (1988) 209–260. [Google Scholar]
  21. J. Warga, Optimal control of differential and functional equations. Academic Press, New York (1972). [Google Scholar]
  22. L.C. Young, Lectures on the calculus of variations and optimal control theory. Chelsea, New York (1980). [Google Scholar]

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