arXiv subjects
Publications and source records attributed to John G. Stalker.
We prove weighted L^2 (Morawetz) estimates for the solutions of linear Schrodinger and wave equation with potentials that decay like |x|^{-2} for large x, by deducing them from estimates on the resolvent of the associated elliptic operator. We then deduce Strichartz estimates for these equations.
Sharp bounds are obtained, under a variety of assumptions on the eigenvalues of the Einstein tensor, for the ratio of the Hawking mass to the areal radius in static, spherically symmetric space-times.
We obtain global space-time weighted-L^2 (Morawetz) and L^4 (Strichartz) estimates for a massless chargeless scalar field propagating on a super-extremal (overcharged) Reissner-Nordstrom background. We begin by discussing the question of well-posedness of the Cauchy problem for scalar fields on non-globally hyperbolic manifolds and the role played by the Friedrichs extension, go over the construction of the function spaces involved, show how to transform the problem to one about the wave equation on the Minkowski space with a singular potential, and finally prove that the potential thus obtained satisfies the various conditions needed in order for the estimates to hold.
We prove spacetime weighted-L^2 estimates for the Schrodinger and wave equation with an inverse-square potential. We then deduce Strichartz estimates for these equations.