Une inégalité de Gårding à bord

Frédéric Hérau

Journées équations aux dérivées partielles (2000)

  • page 1-12
  • ISSN: 0752-0360

Abstract

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The aim of this work is to give a Gårding inequality for pseudodifferential operators acting on functions in L 2 ( ℝ n ) supported in a closed regular region F ⊂ ℝ n . A natural idea is to suppose that the symbol is non-negative in F × ℝ n . Assuming this, we show that this result is true for pseudo-differential operators of order one, when F is the half-space, and under a supplementary weak hypothesis of degeneracy of the symbol on the boundary.

How to cite

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Hérau, Frédéric. "Une inégalité de Gårding à bord." Journées équations aux dérivées partielles (2000): 1-12. <http://eudml.org/doc/93402>.

@article{Hérau2000,
author = {Hérau, Frédéric},
journal = {Journées équations aux dérivées partielles},
keywords = {Gårding inequality for pseudodifferential operators on a manifold with boundary},
language = {fre},
pages = {1-12},
publisher = {Université de Nantes},
title = {Une inégalité de Gårding à bord},
url = {http://eudml.org/doc/93402},
year = {2000},
}

TY - JOUR
AU - Hérau, Frédéric
TI - Une inégalité de Gårding à bord
JO - Journées équations aux dérivées partielles
PY - 2000
PB - Université de Nantes
SP - 1
EP - 12
LA - fre
KW - Gårding inequality for pseudodifferential operators on a manifold with boundary
UR - http://eudml.org/doc/93402
ER -

References

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  2. [2] Bony, J.-M., Sur l'inégalité de Fefferman-Phong, Séminaire sur les Équations aux Dérivées Partielles, 1998-1999, Exp. No. III, École Polytech., Palaiseau, 1998. Zbl1086.35529
  3. [3] Guan, P., C2 a priori estimates for degenerate Monge-Ampère equations, Duke Math. J. (2), 86, (1997), pp 323-346. Zbl0879.35059MR98d:35074
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  5. [5] Hörmander, L., The analysis of linear partial differential operators I, III, Springer-Verlag, Berlin, (1985). Zbl0601.35001
  6. [6] Hwang, I. L., The L2-boundedness of pseudodifferential operators, Trans. Amer. Math. Soc. (1), 302, (1987), pp 55-76. Zbl0651.35089MR88e:47096
  7. [7] Lerner, N., Coherent states and evolution equations, General theory of partial differential equations and microlocal analysis (Trieste, 1995), (Longman), (1996), pp 123-154. Zbl0865.35153MR98a:35151
  8. [8] Lerner, N., The Wick calculus of pseudo-differential operators and energy estimates, New trends in microlocal analysis, (Tokyo, 1995), Springer, (1997), pp. 23-37. Zbl0893.35144MR99i:35187
  9. [9] Lerner, N. et Saint Raymond, X., Une inégalité de Gårding sur une variété à bord, J. Math. Pures Appl. (9), 77, no. 9, (1998), pp. 949-963. Zbl0923.35215MR2000a:35267
  10. [10] Saint Raymond, X., Remarks on Gårding inequalities for differential operators, prépublication Université de nantes, (2000). 

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