In this note we prove some estimates for the resolvent of the operator perturbed by the differential operator
This differential operator is of short range type and a compact perturbation of the Laplacian on . Also we find estimates in the space-time norm for the solution of the wave equation with such perturbation.
Submitted July 12, 2004. Published December 7, 2004.
Math Subject Classifications: 35L05, 35J10, 35P25, 35B25, 35B34, 35B40.
Key Words: Perturbed wave equation; perturbed Schrodinger equation; perturbed Dirac equation; resolvent; short range perturbation; smoothing estimates.
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|Mirko Tarulli |
Dipartimento di Matematica
Universitá di Pisa
Via F. Buonarroti 2, 56127 Pisa, Italy
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