4 papers · 1 filter
Wavenumber-explicit analytic regularity of the heterogeneous Maxwell equations with impedance boundary conditions
Jens Markus Melenk, David Wörgötter
We consider the time-harmonic Maxwell equations at a nonzero wavenumber on a bounded and simply connected Lipschitz domain with an analytic boundary , on…
Length-explicit stability analysis of Helmholtz problems in leaky circular waveguides
Leszek Demkowicz, Martin Halla, Jens Markus Melenk
Motivated by the study and simulation of long, coiled optical fibers we consider in this article a simplified model that is prevalent in the engineering community. Mathematically,…
Regularity of vector fields with piecewise regular curl and divergence
Jens Markus Melenk, David Wörgötter
We consider a bounded Lipschitz domain with sufficiently smooth boundary and prove piecewise Sobolev regularity of vector fields that have piecewise regul…
A note on the shift theorem for the Laplacian in polygonal domains (extended version)
Jens Markus Melenk, Claudio Rojik
We present a shift theorem for solutions of the Poisson equation in a finite planar cone (and hence also on plane polygons) for Dirichlet, Neumann, and mixed boundary conditions. T…