Une inégalité de Gårding à bord
Hérau, Frédéric
Journées équations aux dérivées partielles, (2000), p. 1-12 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

Publié le : 2000-01-01
@article{JEDP_2000____A5_0,
     author = {H\'erau, Fr\'ed\'eric},
     title = {Une in\'egalit\'e de G\aa rding \`a bord},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2000},
     pages = {1-12},
     mrnumber = {2001f:35455},
     zbl = {01808695},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/JEDP_2000____A5_0}
}

Hérau, Frédéric. Une inégalité de Gårding à bord. Journées équations aux dérivées partielles,  (2000), pp. 1-12. http://gdmltest.u-ga.fr/item/JEDP_2000____A5_0/

[1] Bony, J.-M. et Lerner, N., Quantification asymptotique et microlocalisations d'ordre supérieur. I, Ann. Sci. École Norm. Sup. (4), 22, (1989), pp. 377-433. | Numdam | MR 90k:35276 | Zbl 0753.35005

[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. | Zbl 02124223

[3] Guan, P., C2 a priori estimates for degenerate Monge-Ampère equations, Duke Math. J. (2), 86, (1997), pp 323-346. | MR 98d:35074 | Zbl 0879.35059

[4] Hérau F., Opérateurs pseudo-différentiels semi-bornés, Thèse de Doctorat, Rennes, (1999).

[5] Hörmander, L., The analysis of linear partial differential operators I, III, Springer-Verlag, Berlin, (1985). | Zbl 0601.35001

[6] Hwang, I. L., The L2-boundedness of pseudodifferential operators, Trans. Amer. Math. Soc. (1), 302, (1987), pp 55-76. | MR 88e:47096 | Zbl 0651.35089

[7] Lerner, N., Coherent states and evolution equations, General theory of partial differential equations and microlocal analysis (Trieste, 1995), (Longman), (1996), pp 123-154. | MR 98a:35151 | Zbl 0865.35153

[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. | MR 99i:35187 | Zbl 0893.35144

[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. | MR 2000a:35267 | Zbl 0923.35215

[10] Saint Raymond, X., Remarks on Gårding inequalities for differential operators, prépublication Université de nantes, (2000).