Uniform estimates for a class of evolution equations

Matania Ben-Artzi; François Trèves

Journées équations aux dérivées partielles (1992)

  • page 1-12
  • ISSN: 0752-0360

How to cite


Ben-Artzi, Matania, and Trèves, François. "Uniform estimates for a class of evolution equations." Journées équations aux dérivées partielles (1992): 1-12. <http://eudml.org/doc/93251>.

author = {Ben-Artzi, Matania, Trèves, François},
journal = {Journées équations aux dérivées partielles},
keywords = {generalized Schrödinger equations; Airy type equations; estimates; oscillatory integral},
language = {eng},
pages = {1-12},
publisher = {Ecole polytechnique},
title = {Uniform estimates for a class of evolution equations},
url = {http://eudml.org/doc/93251},
year = {1992},

AU - Ben-Artzi, Matania
AU - Trèves, François
TI - Uniform estimates for a class of evolution equations
JO - Journées équations aux dérivées partielles
PY - 1992
PB - Ecole polytechnique
SP - 1
EP - 12
LA - eng
KW - generalized Schrödinger equations; Airy type equations; estimates; oscillatory integral
UR - http://eudml.org/doc/93251
ER -


  1. Ben-Artzi, M. and Devinatz, A. — Local smoothing and convergence properties of Schrödinger-type equations, J. Functional Analysis 101 (1991), 231-245. Zbl0762.35022MR92k:35064
  2. Ben-Artzi, M. and Klainerman, S. — Decay and regularity for the Schrödinger equation, J. d'Analyse Math. (1992), to appear. Zbl0802.35057
  3. Constantin, P. and Saut, J. C. — Local smoothing properties for dispersive equations, J. Amer. Math. Soc. 1 (1988), 413-439. Zbl0667.35061MR89d:35150
  4. Journé, J. L., Soffer, A. and Sogge, C. D. — Decay estimates for Schrödinger operators, Comm. Pure and Applied Math. (1992), to appear. Zbl0743.35008
  5. Kato, T. — Perturbation Theory for Linear Operators, Springer 1976. Zbl0342.47009MR53 #11389
  6. Kato, T. — Nonlinear Schrödinger equations, in “Schrödinger Operators”, H. Holden and A. Jensen editors, Springer Lecture Notes in Physics ͅ, 1989. Zbl0698.35131
  7. Kenig, C. E., Ponce, G. and Vega, L. — Oscillatory integrals and regularity of dispersive equations, Indiana Univ. J. 40 (1991), 33-69. Zbl0738.35022MR92d:35081
  8. Phong, D. H. and Stein, E. M. — Oscillatory integrals with polynomial phases, (1991), preprint. Zbl0829.42014
  9. Sidi, A., Sulem C. and Sulem, P. L., On the long time behaviour of a generalized KdV equation, Acta Applicandae Math. 7 (1986), 35-47. Zbl0625.35072MR87k:35038
  10. Strichartz, R. — Restriction of Fourier Transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), 705-714. Zbl0372.35001MR58 #23577
  11. Strichartz, R. — Asymptotic behavior of waves, J. Functional Analysis 40 (1981), 341-357. Zbl0484.35070MR82j:35020
  12. Tomas, P. — Arestriction theorem for the Fourier transform, Bull. Amer. Math. Soc. 81 (1975), 447-478. Zbl0298.42011MR50 #10681
  13. Tsutsumi, Y. — L2-solutions for nonlinear Schrödinger equations and nonlinear groups, Funkcial. Ekvac. 30 (1987), 115-125. Zbl0638.35021MR89c:35143
  14. Tsutsumi, Y. — Glocal strong solutions for nonlinear Schrödinger equations, Nonlinear Anal. 11 (1987), 1143-1154. Zbl0657.35032MR88m:35144

NotesEmbed ?


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.