Electron. J. Diff. Eqns., Vol. 2004(2004), No. 146, pp. 1-14.

Resolvent estimates for scalar fields with electromagnetic perturbation

Mirko Tarulli

Abstract:
In this note we prove some estimates for the resolvent of the operator $-\Delta$ perturbed by the differential operator
$$ V(x,D)=ia(x)\cdot \nabla+V(x)\quad \hbox{in }\mathbb{R}^3\,. $$
This differential operator is of short range type and a compact perturbation of the Laplacian on $\mathbb{R}^3$. 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
email: tarulli@mail.dm.unipi.it

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