Local regularity of solutions to wave equations with time-dependent potentials
The authors continue the investigation they started in the proceeding paper [\textit{A. Ruiz} and \textit{L. Vega}, Int. Math. Res. Not. 1993, No. 1, 13-27 (1993; Zbl 0812.35016)]. Here, they give the weighted estimates of the solutions to the initial value problems for the time-dependent Schrödinger equation and for the wave equation in the Lorentz spaces. Using the above results they prove the local existence, uniqueness and regularity of the above problems perturbed by time-dependent potentials with singularities.
time-dependent potentials with singularities
scientific article; zbMATH DE number 755401
scientific article