5 papers
Dispersive estimates for Schrödinger's and wave equations on Riemannian manifolds
Marius Beceanu
This paper proves decay estimates for Schrödinger's and wave equations with scalar potentials on three-dimensional Riemannian manifolds. The main result regards small perturb…
Decay estimates for Schrödinger's equation with magnetic potentials in three dimensions
Marius Beceanu, Hyun-Kyoung Kwon
In this paper we prove that Schrödinger's equation with a Hamiltonian of the form , which includes a magnetic potential , has the same dispersiv…
Local Exact Controllability to Stationary Solutions of a Semilinear Parabolic Equation
Marius Beceanu
This paper establishes the local exact controllability of the quasilinear porous media equation with Dirichlet boundary condition.\\ Consider the equation $$\begin{aligned} &y_t -…
Pluriharmonic solutions to Yang-Mills equations: a -algebras approach
Marius Beceanu, Sachin Munshi, Rongwei Yang
This partially expository paper provides a view of Yang-Mills equations from the perspective of complex variables, operator theory, and -algebras. Through operator-valued pl…
The Eigenvalue Problem for the Laplacian via Conformal Mapping and the Gohberg--Sigal Theory
Marius Beceanu, Jiho Hong, Hyun-Kyoung Kwon +1
We consider the Dirichlet and Neumann eigenvalues of the Laplacian for a planar, simply connected domain. The eigenvalues admit a characterization in terms of a layer potential of…