Lösung der Dirichletproblems und Konvergenz der Differenzenapproximation für elliptische Differentialgleichungen zweiter Ordnung.
Lower and upper bounds for the Rayleigh conductivity of a perforated plate
Lower and upper bounds for the Rayleigh conductivity of a perforation in a thick plate are usually derived from intuitive approximations and by physical reasoning. This paper addresses a mathematical justification of these approaches. As a byproduct of the rigorous handling of these issues, some improvements to previous bounds for axisymmetric holes are given as well as new estimates for tilted perforations. The main techniques are a proper use of the Dirichlet and Kelvin variational principlesin...
Lp regularity of the Dirichlet problem for elliptic equations with singular drift.