Remarks on Gårding inequalities for differential operators

Xavier Saint Raymond

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 1, page 169-185
  • ISSN: 0391-173X

Abstract

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Classical Gårding inequalities such as those of Hörmander, Hörmander-Melin or Fefferman-Phong are proved by pseudo-differential methods which do not allow to keep a good control on the supports of the functions under study nor on the smoothness of the coefficients of the operator. In this paper, we show by very simple calculations that in certain special situations, the results that can be obtained directly are much better than those expected thanks to the general theory.

How to cite

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Saint Raymond, Xavier. "Remarks on Gårding inequalities for differential operators." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.1 (2002): 169-185. <http://eudml.org/doc/84462>.

@article{SaintRaymond2002,
abstract = {Classical Gårding inequalities such as those of Hörmander, Hörmander-Melin or Fefferman-Phong are proved by pseudo-differential methods which do not allow to keep a good control on the supports of the functions under study nor on the smoothness of the coefficients of the operator. In this paper, we show by very simple calculations that in certain special situations, the results that can be obtained directly are much better than those expected thanks to the general theory.},
author = {Saint Raymond, Xavier},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Fefferman-Phong inequality; paradifferential calculus; lower bounds for operators with nonnegative principal symbol},
language = {eng},
number = {1},
pages = {169-185},
publisher = {Scuola normale superiore},
title = {Remarks on Gårding inequalities for differential operators},
url = {http://eudml.org/doc/84462},
volume = {1},
year = {2002},
}

TY - JOUR
AU - Saint Raymond, Xavier
TI - Remarks on Gårding inequalities for differential operators
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2002
PB - Scuola normale superiore
VL - 1
IS - 1
SP - 169
EP - 185
AB - Classical Gårding inequalities such as those of Hörmander, Hörmander-Melin or Fefferman-Phong are proved by pseudo-differential methods which do not allow to keep a good control on the supports of the functions under study nor on the smoothness of the coefficients of the operator. In this paper, we show by very simple calculations that in certain special situations, the results that can be obtained directly are much better than those expected thanks to the general theory.
LA - eng
KW - Fefferman-Phong inequality; paradifferential calculus; lower bounds for operators with nonnegative principal symbol
UR - http://eudml.org/doc/84462
ER -

References

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  1. [1] J.-M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non-linéaires, Ann. Sci. École Norm. Sup. Paris (4) 14 (1981), 209-246. Zbl0495.35024MR631751
  2. [2] J.-M. Bony, “Sur l’inégalité de Fefferman-Phong”, exposé No III, Séminaire sur les Équations aux dérivées partielles 1998-99, École Polytechnique, Palaiseau (France) 1999. Zbl1086.35529MR1721321
  3. [3] F. Hérau, “Opérateurs différentiels semi-bornés”, thèse de doctorat, Rennes (France) septembre 1999. 
  4. [4] L. Hörmander, “Linear partial differential operators”, Springer, Berlin, 1963. Zbl0108.09301
  5. [5] L. Hörmander, “The analysis of linear partial differential operators III”, Springer, Berlin, 1985. Zbl0601.35001MR781536
  6. [6] L. Hörmander, Pseudo-differential operators of type 1,1 ( Theorem 7 . 1 ) , Comm. Partial Differential Equations 13 (1988), 1085-1111. Zbl0667.35078MR946283
  7. [7] N. Lerner – X. Saint Raymond, Une inégalité de Gårding sur une variété à bord, J. Math. Pures Appl. 77 (1998), 949-963. Zbl0923.35215MR1656764

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