Smoothing Effect for Schrödinger Boundary Value Problems

Inverse Boundary Value Problems for the Magnetic Schrödinger Equation

We survey recent results on inverse boundary value problems for the magnetic Schrödinger equation.

Convergence of nonconforming V-cycle and F-cycle multigrid algorithms for second order elliptic boundary value problems

The convergence of V -cycle and F -cycle multigrid algorithms with a sufficiently large number of smoothing steps is established for nonconforming finite element methods for second order elliptic boundary value problems.

Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

Well posedness and smoothing effect of Schrödinger-Poisson equation

The Derivative Nonlinear Schrödinger Equation on the Half Line

We study the initial-boundary value problem for the derivative nonlinear Schrödinger (DNLS) equation. More precisely we study the wellposedness theory and the regularity properties of the DNLS equation on the half line. We prove almost sharp local wellposedness, nonlinear smoothing, and small data global wellposedness in the energy space. One of the obstructions is that the crucial gauge transf...