Pauli operators and the $\overline\partial$-Neumann problem

The Regularity and Neumann Problem for Non-symmetric Elliptic Operators

We establish optimal Lp bounds for the non-tangential maximal function of the gradient of the solution to a second-order elliptic operator in divergence form, possibly non-symmetric, with bounded measurable coefficients independent of the vertical variable, on the domain above a Lipschitz graph in the plane, in terms of the Lp-norm at the boundary of the tangential derivative of the Dirichlet d...

On the zero modes of Pauli operators

Compactness in the ∂-neumann Problem, Magnetic Schrödinger Operators, and the Aharonov-bohm Effect

Compactness of the Neumann operator in the ∂̄-Neumann problem is studied for weakly pseudoconvex bounded Hartogs domains in two dimensions. A nonsmooth domain is constructed for which condition (P) fails to hold, yet the Kohn Laplacian still has compact resolvent. The main result, in contrast, is that for smoothly bounded Hartogs domains, the well-known sufficient condition (P) is equivalent to ...

A Boundary Meshless Method for Neumann Problem

Boundary integral equations (BIE) are reformulations of boundary value problems for partial differential equations. There is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. In this paper, the Neumann problem is reformulated to a BIE, and then moving least squares as a meshless method is describe...

Möbius Pairs of Simplices and Commuting Pauli Operators

There exists a large class of groups of operators acting on Hilbert spaces, where commutativity of group elements can be expressed in the geometric language of symplectic polar spaces embedded in the projective spaces PG(n, p), n being odd and p a prime. Here, we present a result about commuting and non-commuting group elements based on the existence of socalled Möbius pairs of n-simplices, i. ...