The aim of this work is to give a Gårding inequality for pseudodifferential operators acting on functions in supported in a closed regular region . A natural idea is to suppose that the symbol is non-negative in . Assuming this, we show that this result is true for pseudo-differential operators of order one, when is the half-space, and under a supplementary weak hypothesis of degeneracy of the symbol on the boundary.
@incollection{JEDP_2000____A5_0, author = {H\'erau, Fr\'ed\'eric}, title = {Une in\'egalit\'e de {G\r{a}rding} \`a bord}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {5}, pages = {1--12}, publisher = {Universit\'e de Nantes}, year = {2000}, mrnumber = {2001f:35455}, zbl = {01808695}, language = {fr}, url = {http://archive.numdam.org/item/JEDP_2000____A5_0/} }
Hérau, Frédéric. Une inégalité de Gårding à bord. Journées équations aux dérivées partielles (2000), article no. 5, 12 p. http://archive.numdam.org/item/JEDP_2000____A5_0/
[1] Quantification asymptotique et microlocalisations d'ordre supérieur. I, Ann. Sci. École Norm. Sup. (4), 22, (1989), pp. 377-433. | Numdam | MR | Zbl
et ,[2] Sur l'inégalité de Fefferman-Phong, Séminaire sur les Équations aux Dérivées Partielles, 1998-1999, Exp. No. III, École Polytech., Palaiseau, 1998. | Zbl
,[3] C2 a priori estimates for degenerate Monge-Ampère equations, Duke Math. J. (2), 86, (1997), pp 323-346. | MR | Zbl
,[4] Opérateurs pseudo-différentiels semi-bornés, Thèse de Doctorat, Rennes, (1999).
,[5] The analysis of linear partial differential operators I, III, Springer-Verlag, Berlin, (1985). | Zbl
,[6] The L2-boundedness of pseudodifferential operators, Trans. Amer. Math. Soc. (1), 302, (1987), pp 55-76. | MR | Zbl
,[7] Coherent states and evolution equations, General theory of partial differential equations and microlocal analysis (Trieste, 1995), (Longman), (1996), pp 123-154. | MR | Zbl
,[8] The Wick calculus of pseudo-differential operators and energy estimates, New trends in microlocal analysis, (Tokyo, 1995), Springer, (1997), pp. 23-37. | MR | Zbl
,[9] Une inégalité de Gårding sur une variété à bord, J. Math. Pures Appl. (9), 77, no. 9, (1998), pp. 949-963. | MR | Zbl
et ,[10] Remarks on Gårding inequalities for differential operators, prépublication Université de nantes, (2000).
,