Resolvent estimates for scalar fields with electromagnetic perturbation.

Tarulli, Mirko

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Resolvent estimates and the decay of the solution to the wave equation with potential

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We prove a weighted $L^{\infty}$ estimate for the solution to the linear wave equation with a smooth positive time independent potential. The proof is based on application of generalized Fourier transform for the perturbed Laplace operator and a finite dependence domain argument. We apply this estimate to prove the existence of global small data solution to supercritical semilinear wave equations with potential.