Second order differentiability and Lipschitz smooth points of convex functionals

Eva Matoušková; Luděk Zajíček

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 4, page 617-640
  • ISSN: 0011-4642

How to cite

top

Matoušková, Eva, and Zajíček, Luděk. "Second order differentiability and Lipschitz smooth points of convex functionals." Czechoslovak Mathematical Journal 48.4 (1998): 617-640. <http://eudml.org/doc/30442>.

@article{Matoušková1998,
author = {Matoušková, Eva, Zajíček, Luděk},
journal = {Czechoslovak Mathematical Journal},
keywords = {Hilbert space; convex function; second order differentiability; Lipschitz smoothness; Aronszajn null set; Haar null set},
language = {eng},
number = {4},
pages = {617-640},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Second order differentiability and Lipschitz smooth points of convex functionals},
url = {http://eudml.org/doc/30442},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Matoušková, Eva
AU - Zajíček, Luděk
TI - Second order differentiability and Lipschitz smooth points of convex functionals
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 4
SP - 617
EP - 640
LA - eng
KW - Hilbert space; convex function; second order differentiability; Lipschitz smoothness; Aronszajn null set; Haar null set
UR - http://eudml.org/doc/30442
ER -

References

top
  1. 10.4064/sm-57-2-147-190, Studia Math. 57 (1976), 147–190. (1976) Zbl0342.46034MR0425608DOI10.4064/sm-57-2-147-190
  2. Geometric Non-linear Functional Analysis, to appear. (to appear) 
  3. 10.1090/S0002-9947-1994-1145959-4, Trans. Amer. Math. Soc. 342 (1994), 43–82. (1994) MR1145959DOI10.1090/S0002-9947-1994-1145959-4
  4. 10.4153/CJM-1989-032-7, Canad. J. Math. 41 (1989), 702–720. (1989) MR1012624DOI10.4153/CJM-1989-032-7
  5. Topology and Borel Structure, North-Holland, Amsterdam, 1974. (1974) Zbl0273.28001MR0348724
  6. 10.4064/fm-144-1-73-88, Fundam. Math. 144 (1994), 73–88. (1994) Zbl0842.43006MR1271479DOI10.4064/fm-144-1-73-88
  7. Linear Operators I, Interscience Publishers, New York, 1967. (1967) 
  8. Lipschitz smooth points of convex functions and isomorphic characterisation of Hilbert spaces, Proc. London Math. Soc. 51 (1985), 113–126. (1985) MR0788852
  9. Topology I, Academic Press, London, 1968. (1968) 
  10. 10.2307/2373874, Amer. J. Math. 100 (1978), 19–41. (1978) Zbl0384.28005MR0507445DOI10.2307/2373874
  11. Konvexe Mengen, Springer-Verlag, Berlin, 1980. (1980) MR0586235
  12. 10.1007/BF02757715, Israel J. Math. 19 (1974), 217–219. (1974) MR0367810DOI10.1007/BF02757715
  13. A highly non-smooth norm on Hilbert space, (to appear). (to appear) MR1715018
  14. A characterization of reflexive Banach spaces, Proc. Amer. Math. Soc (to appear). (to appear) MR1301517
  15. Convex Functions, Monotone Operators and Differentiabilitypubl Lecture Notes in Math. 1364, Springer-Verlag, Berlin, 1993. (1993) MR1238715
  16. Convex integral functionals and duality, Contributions to nonlinear functional analysis, E.H. Zarantello (ed.), New York, London, 1971, pp. 215–236. (1971) Zbl0295.49006MR0390870
  17. Integral functionals, normal integrands and measurable selections, Nonlinear operators and the calculus of variations, Lecture Notes in Math. 543, A. Dold and B. Eckmann (eds.), Bruxeles, 1975, pp. 157–207. (1975) MR0512209
  18. Hausdorff Measures, Cambridge Univ. Press, Cambridge, 1970. (1970) Zbl0204.37601MR0281862
  19. On Haar null sets, Fundam. Math. 149 (1996), 205–210. (1996) Zbl0887.28006MR1383206
  20. Delta-convex mappings between Banach spaces and applications, Dissertationes Math. CCLXXXIX, (1989), 48. (1989) MR1016045

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.