Free Access
Issue
ESAIM: COCV
Volume 15, Number 1, January-March 2009
Page(s) 68 - 101
DOI https://doi.org/10.1051/cocv:2008067
Published online 23 January 2009
  1. J.A. Andrejewa and R. Klötzler, Zur analytischen Lösung geometrischer Optimierungsaufgaben mittels Dualität bei Steuerungsproblemen. Teil I. Z. Angew. Math. Mech. 64 (1984) 35–44. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.A. Andrejewa and R. Klötzler, Zur analytischen Lösung geometrischer Optimierungsaufgaben mittels Dualität bei Steuerungsproblemen. Teil II. Z. Angew. Math. Mech. 64 (1984) 147–153. [CrossRef] [MathSciNet] [Google Scholar]
  3. G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. 2nd Edn., Springer, New York etc. (2006). [Google Scholar]
  4. J.M. Ball and F. Murat, Formula -quasiconvexity and variational problems for multiple integrals. J. Funct. Anal. 58 (1984) 225–253. [Google Scholar]
  5. A. Brøndsted, An Introduction to Convex Polytopes. Springer, New York - Heidelberg - Berlin (1983). [Google Scholar]
  6. C. Brune, H. Maurer and M. Wagner, Edge detection within optical flow via multidimensional control. BTU Cottbus, Preprint-Reihe Mathematik, Preprint Nr. M-02/2008 (submitted). [Google Scholar]
  7. C. Carathéodory, Vorlesungen über reelle Funktionen. 3rd Edn., Chelsea, New York (1968). [Google Scholar]
  8. E. Casadio Tarabusi, An algebraic characterization of quasi-convex functions. Ricerche di Mat. 42 (1993) 11–24. [Google Scholar]
  9. F.H. Clarke, Optimization and Nonsmooth Analysis. 2nd Edn., SIAM, Philadelphia (1990). [Google Scholar]
  10. L. Collatz and W. Wetterling, Optimierungsaufgaben, 2nd Edn., Heidelberger Taschenbücher 15. Springer, Berlin - Heidelberg - New York (1971). [Google Scholar]
  11. B. Dacorogna, Quasiconvexity and relaxation of nonconvex problems in the calculus of variations. J. Funct. Anal. 46 (1982) 102–118. [CrossRef] [MathSciNet] [Google Scholar]
  12. B. Dacorogna, Direct Methods in the Calculus of Variations. 2nd Edn., Springer, New York etc. (2008). [Google Scholar]
  13. B. Dacorogna and N. Fusco, Semi-continuité des fonctionnelles avec contraintes du type “Formula ". Boll. Un. Mat. Ital. B (6) 4 (1985) 179–189. [MathSciNet] [Google Scholar]
  14. B. Dacorogna and P. Marcellini, General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial case. Acta Math. 178 (1997) 1–37. [CrossRef] [MathSciNet] [Google Scholar]
  15. B. Dacorogna and P. Marcellini, Cauchy-Dirichlet problem for first order nonlinear systems. J. Funct. Anal. 152 (1998) 404–446. [Google Scholar]
  16. B. Dacorogna and P. Marcellini, Implicit Partial Differential Equations. Birkhäuser, Boston - Basel - Berlin (1999). [Google Scholar]
  17. B. Dacorogna and A.M. Ribeiro, On some definitions and properties of generalized convex sets arising in the calculus of variations, in Recent Advances on Elliptic and Parabolic Issues, M. Chipot and H. Ninomiya Eds., Proceedings of the 2004 Swiss-Japanese Seminar: Zurich, Switzerland, 6–10 December 2004, World Scientific, Singapore (2006) 103–128. [Google Scholar]
  18. R. De Arcangelis and E. Zappale, The relaxation of some classes of variational integrals with pointwise continuous-type gradient constraints. Appl. Math. Optim. 51 (2005) 251–257. [CrossRef] [MathSciNet] [Google Scholar]
  19. R. De Arcangelis, S. Monsurrò and E. Zappale, On the relaxation and the Lavrentieff phenomenon for variational integrals with pointwise measurable gradient constraints. Calc. Var. Partial Differential Equations 21 (2004) 357–400. [CrossRef] [MathSciNet] [Google Scholar]
  20. I. Ekeland and R. Témam, Convex Analysis and Variational Problems. 2nd Edn., SIAM, Philadelphia (1999). [Google Scholar]
  21. J. Elstrodt, Maß- und Integrationstheorie. Springer, New York - Heidelberg - Berlin (1996). [Google Scholar]
  22. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton etc. (1992). [Google Scholar]
  23. A.D. Ioffe and V.M. Tichomirow, Theorie der Extremalaufgaben. VEB Deutscher Verlag der Wissenschaften, Berlin (1979). [Google Scholar]
  24. B. Kawohl, From Mumford-Shah to Perona-Malik in image processing. Math. Meth. Appl. Sci. 27 (2004) 1803–1814. [CrossRef] [MathSciNet] [Google Scholar]
  25. D. Kinderlehrer and P. Pedregal, Characterizations of Young measures generated by gradients. Arch. Rat. Mech. Anal. 115 (1991) 329–365. [CrossRef] [MathSciNet] [Google Scholar]
  26. J. Kristensen, On the non-locality of quasiconvexity. Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999) 1–13. [CrossRef] [MathSciNet] [Google Scholar]
  27. J.B. Kruskal, Two convex counterexamples: A discontinuous envelope function and a nondifferentiable nearest-point mapping. Proc. Amer. Math. Soc. 23 (1969) 697–703. [CrossRef] [MathSciNet] [Google Scholar]
  28. M. Kružík, Bauer's maximum principle and hulls of sets. Calc. Var. Partial Differential Equations 11 (2000) 321–332. [CrossRef] [MathSciNet] [Google Scholar]
  29. M. Kružík, Quasiconvex extreme points of convex sets, in Elliptic and Parabolic Problems, J. Bemelmans, B. Brighi, A. Brillard, M. Chipot, F. Conrad, I. Shafrir, V. Valente and G. Vergara-Caffarelli Eds., World Scientific Publishing, River Edge (2002) 145–151. [Google Scholar]
  30. K.A. Lur'e, Hayka, Moscow (1975). [Google Scholar]
  31. C.B. Morrey, Quasi-convexity and the lower semicontinuity of multiple integrals. Pacific J. Math. 2 (1952) 25–53. [CrossRef] [MathSciNet] [Google Scholar]
  32. S. Pickenhain and M. Wagner, Piecewise continuous controls in Dieudonné-Rashevsky type problems. J. Optim. Theory Appl. 127 (2005) 145–163. [CrossRef] [MathSciNet] [Google Scholar]
  33. R.T. Rockafellar, Convex Analysis. 2nd Edn., Princeton University Press, Princeton (1972). [Google Scholar]
  34. R.T. Rockafellar and R.J.-B. Wets, Variational Analysis, Grundlehren 317. Springer, Berlin etc. (1998). [Google Scholar]
  35. R. Schneider, Convex Bodies: The Brunn-Minkowski Theory. Cambridge University Press, Cambridge (1993). [Google Scholar]
  36. K. Schulz and B. Schwartz, Finite extensions of convex functions. Math. Operationsforschung Statist. Ser. Optimization 10 (1979) 501–509. [Google Scholar]
  37. V. Šverák, Rank-one convexity does not imply quasiconvexity. Proc. Roy. Soc. Edinburgh Ser. A 120 (1992) 185–189. [Google Scholar]
  38. T.W. Ting, Elastic-plastic torsion of convex cylindrical bars. J. Math. Mech. 19 (1969) 531–551. [MathSciNet] [Google Scholar]
  39. T.W. Ting, Elastic-plastic torsion problem III. Arch. Rat. Mech. Anal. 34 (1969) 228–244. [CrossRef] [Google Scholar]
  40. M. Wagner, Erweiterungen des mehrdimensionalen Pontrjaginschen Maximumprinzips auf meßbare und beschränkte sowie distributionelle Steuerungen. Ph.D. thesis, Universität Leipzig, Germany (1996). [Google Scholar]
  41. M. Wagner, Nonconvex relaxation properties of multidimensional control problems, in Recent Advances in Optimization, A. Seeger Ed., Lecture Notes in Economics and Mathematical Systems 563, Springer, Berlin etc. (2006) 233–250. [Google Scholar]
  42. M. Wagner, Mehrdimensionale Steuerungsprobleme mit quasikonvexen Integranden. Habilitation thesis, Brandenburgische Technische Universität Cottbus, Cottbus, Germany (2006). [Google Scholar]
  43. M. Wagner, Pontryagin's maximum principle for multidimensional control problems in image processing. J. Optim. Theory Appl. (to appear). [Google Scholar]
  44. K. Zhang, On the structure of quasiconvex hulls. Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 663–686. [CrossRef] [MathSciNet] [Google Scholar]
  45. K. Zhang, On the quasiconvex exposed points. ESAIM: COCV 6 (2001) 1–19 (electronic). [CrossRef] [EDP Sciences] [Google Scholar]

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