Johns Hopkins University

most citedMagnetically driven ferroelectric order in Ni

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math.AP2005★ 36 cited

A counterexample to dispersive estimates for Schrödinger operators in higher dimensions

M. Goldberg, M. Visan

In dimension $n > 3$ we show the existence of a compactly supported potential in the differentiability class $C^{α}$ , $α < \frac{n - 3}{2}$ , for which the solutions to the linear Schrödinge…

math.AP2004

Nonlinear hyperbolic equations in infinite homogeneous waveguides

Jason Metcalfe, Christopher D. Sogge, Ann Stewart

In this paper we prove global and almost global existence theorems for nonlinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides. We can handle both…

math.AP2004

Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition

Jason Metcalfe, Makoto Nakamura, Christopher D. Sogge

We prove global existence of solutions to multiple speed, Dirichlet-wave equations with quadratic nonlinearities satisfying the null condition in the exterior of compact obstacles.…

math.AP2004

Global existence of solutions to multiple speed systems of quasilinear wave equations in exterior domains

Jason Metcalfe, Makoto Nakamura, Christopher D. Sogge

In this paper we prove global existence for certain multispeed Dirichlet-wave equations with quadratic nonlinearities outside of obstacles. We assume the natural null condition for…

math.AP2004★ 9 cited

Dispersive Bounds for the three-dimensional Schrodinger equation with almost critical potentials

Michael Goldberg

We prove a dispersive estimate for the time-independent Schrodinger operator H = -Δ+ V in three dimensions. The potential V(x) is assumed to lie in the intersection L^p(R^3) \cap L…