The University of Tokyo

most citedSpin current and magneto-electric effect in non-collinear magnets

2.2k citations

Showing math.APShow all

3 papers · 1 filter

math.AP2005★ 30 cited

Cross-shaped and Degenerate Singularities in an Unstable Elliptic Free Boundary Problem

J. Andersson, G. S. Weiss

We investigate singular and degenerate behavior of solutions of the unstable free boundary problem $Δ u = - χ_{{u > 0}} .$ First, we construct a solution that is not of class $C^{1…

math.AP2005★ 3 cited

An Unstable Elliptic Free Boundary Problem arising in Solid Combustion

Regis Monneau, G. S. Weiss

We prove a regularity result for the unstable elliptic free boundary problem $Δ u = - χ_{{u > 0}}$ related to traveling waves in a problem arising in solid combustion. The maximal so…

math.AP2005★ 1 cited

The Two-Phase Membrane Problem -- an Intersection-Comparison Approach to the Regularity at Branch Points

Henrik Shahgholian, Georg S. Weiss

For the two-phase membrane problem $Δ u = \frac{λ _{+}}{2} χ_{{u > 0}} - \frac{λ _{-}}{2} χ_{{u < 0}},$ where $λ_{+} > 0$ and $λ_{-} > 0,$ we prove in two dimensions that the free boundary is i…