Abstract

The space of directional-morphological transitions is analyzed and a tangential regularity result is established for the subset V\mathcal{V}. This subset arises in a natural way when one considers viability problems where both, trajectories and constraints, are evolving in time governed by differential and morphological equations, respectively. Furthermore a control problem associated with this kind of evolutionary-morphological systems is studied.

Author information

Contact details are reproduced from the original publication and may be historical.

José Alberto Murillo Hernández

Dep. de Matemática Aplicada y Estadística, Universidad Politécnica, Paseo de Alfonso XIII s/n, 30203 Cartagena, Spain

alberto.murillo@upct.es

Keywords

  • Tangential regularity
  • morphological equations
  • differential inclusions
  • constrained control systems

References

  1. J.-P. Aubin: Viability Theory, Birkhäuser, Boston (1991).Google Scholar
  2. J.-P. Aubin: Mutational and Morphological Analysis. Tools for Shape Evolution and Morphogenesis, Birkhäuser, Boston (1999).https://doi.org/10.1007/978-1-4612-1576-9Google Scholar
  3. J.-P. Aubin, A. Bayen, N. Bonneuil, P. Saint-Pierre: Viability, Control and Games: Regulation of Complex Evolutionary Systems Under Uncertainty and Viability Constraints, Springer, to appear.Google Scholar
  4. J.-P. Aubin, H. Frankowska: Set-Valued Analysis, Birkhäuser, Boston (1990).Google Scholar
  5. J.-P. Aubin, J. A. Murillo: Morphological equations and sweeping processes, in: Nonsmooth Mechanics and Analysis. Theoretical and Numerical Advances, P. Alart, O. Maisonneuve, R. T. Rockafellar (eds.), Springer, New York (2006) 249–259.Google Scholar
  6. G. Beer: Topologies on Closed and Closed Convex Sets, Kluwer, Dordrecht (1993).https://doi.org/10.1007/978-94-015-8149-3Google Scholar
  7. C. Calcaterra, D. Bleecker: Generating flows on metric spaces, J. Math. Anal. Appl. 248 (2000) 645–677.https://doi.org/10.1006/jmaa.2000.6948Google Scholar
  8. C. Castaing, M. Valadier: Convex Analysis and Measurable Multifunctions, Springer, Berlin (1977).https://doi.org/10.1007/BFb0087685Google Scholar
  9. L. Doyen: Filippov and invariance theorems for mutational inclusions of tubes, Set-Valued Anal. 1 (1993) 289–303.https://doi.org/10.1007/BF01027639Google Scholar
  10. L. Doyen: Mutational equations for shapes and vision-based control, J. Math. Imaging Vis. 5 (1995) 99–109.https://doi.org/10.1007/BF01250522Google Scholar
  11. A. F. Filippov: Classical solutions of differential equations with multivalued right-hand side, SIAM J. Control 5 (1967) 609–621.https://doi.org/10.1137/0305040Google Scholar
  12. S. Gautier, K. Pichard: Viability results for mutational equations with delay, Numer. Funct. Anal. Optim. 24 (2003) 273–284.https://doi.org/10.1081/NFA-120022922Google Scholar
  13. T. Lorenz: Set-valued maps for image segmentation, Comput. Visual Sci. 4 (2001) 41–57.https://doi.org/10.1007/s007910100056Google Scholar
  14. K. Pichard: Équations Différentielles dans les Espaces Métriques. Application à l’Évolution de Domaines, Thèse de l’Université de Pau (2001).Google Scholar
  15. R. T. Rockafellar, R. J.-B. Wets: Variational Analysis, Springer, Berlin (1998).https://doi.org/10.1007/978-3-642-02431-3Google Scholar

Suggested citation

J. A. Murillo Hernández. “Tangential Regularity in the Space of Directional-Morphological Transitions.” Journal of Convex Analysis 13 (2006), No. 2, 423–441. https://doi.org/10.68381/jca13033

Download BibTeXPublished by Heldermann Verlag.

Published by Heldermann Verlag, 2006. Rights now held by Banach Press LLC.