* Partially supported by CNPq (Brazil) We study the distribution of the (complex) eigenvalues for interior boundary value problems with dissipative boundary conditions in the case of C 1 -smooth boundary under some natural assumption on the behaviour of the geodesics. As a consequence we obtain energy decay estimates of the solutions of the corresponding wave equation.
2000 Mathematics Subject Classification: 35L15, 35B40, 47F05. We prove dispersive estimates for solutions to the wave equation with a real-valued potential V.
2000 Mathematics Subject Classification: 35L15, 35B40, 47F05. Introduction and statement of results. In the present paper we will be interested in studying the decay properties of the Schrödinger group. The authors have been supported by the agreement Brazil-France in Mathematics – Proc. 69.0014/01-5. The first two authors have also been partially supported by the CNPq-Brazil.
Pseudodifferential operators are studied, from the viewpoint of local solvability and under the assumption that, micro-locally, the principal symbol factorizes as with elliptic, homogeneous of degree , and homogeneous of degree one, satisfying the following condition : there is a point in the characteristic variety and a complex number such that at and such that the restriction of to the bicharacteristic strip of vanishes of order at , changing sign there from minus to...
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