Space-time estimates for the wave equations with singular potentials
The IVP for the wave equation with a time dependent potential \(V(x, t)\) is considered. The potential is allowed to have a singularity in the origin of the coordinates, is not necessarily differentiable but its supremum over all \(t\) has to be bounded by a special function depending on spatial dimension \(n\) and space variable \(x\). The dimension \(n\) is considered greater or equal to 3. In case the initial conditions belong to some Sobolev spaces, one proves the local regularity of solution and additional the Strichartz type estimate.
scientific article; zbMATH DE number 5349084
scientific article