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A Gårding inequality with boundary. (Une inégalité de Gårding à bord.) (French) Zbl 1034.35169

Proceedings of the conference on partial differential equations, La Chapelle sur Erdre, France, Nantes, June 5–9, 2000. Exp. Nos. I-XX. Nantes: Université de Nantes (ISBN 2-86939-157-9/pbk). Exp. No. 5, 12 p. (2000).
The author proves a Gårding inequality for pseudodifferential operators on a manifold \(M\) with boundary. Namely, assume \(M=\{x= (x_1,x'), x_1\geq 0\}\), \(a\in S^1_{1,0}\), \(a\geq 0\) on \(M\). Supposing that \(\partial a/ \partial x_1(0,x',\xi)= 0\) implies \(\partial^2a/ \partial x_1\partial x'(0,x',\xi)= \partial^2a/ \partial x_1\partial\xi(0,x',\xi)=0\), the author obtains \[ \text{Re}\bigl(a(x,D)u,u\bigr) \geq-C\| u \|^2 \] for every \(u\in S(\mathbb{R}^n)\) with \(\text{supp}\,u\subset M\).
For the entire collection see [Zbl 0990.00045].

MSC:

35S05 Pseudodifferential operators as generalizations of partial differential operators
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