Lp-Lq estimates for electromagnetic Helmholtz equation

Abstract

In space dimension n>=3, we consider the electromagnetic Schrödinger hamiltonian H = (∇ − i A(x))2 − V and the corresponding Helmholtz equation (∇ − i A(x))2u + u − V (x)u = f in Rn. We extend the well-known L p –L q estimates for the solution of the free Helmholtz equation to the case when the electromagnetic hamiltonian H is considered.