Resolvent estimates for scalar fields with electromagnetic perturbation
Texas State University-San Marcos, Department of Mathematics
In this note we prove some estimates for the resolvent of the operator -Δ perturbed by the differential operator V(x, D) = iα(x) ∙ ∇ + V(x) in ℝ3. This differential operator is of short range type and a compact perturbation of the Laplacian on ℝ3. Also we find estimates in the space-time norm for the solution of the wave equation with such perturbation.
Perturbed wave equation, Perturbed Schrödinger equation, Perturbed Dirac equation, Resolvent, Short range perturbation, Smoothing estimates
Tarulli, M. (2004). Resolvent estimates for scalar fields with electromagnetic perturbation. <i>Electronic Journal of Differential Equations, 2004</i>(146), pp. 1-14.