H. Shahgholian

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

1 citations · 1 across the 1 of their papers we have counts for

collaborators

2 papers

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…

math.AP2000

Regularity of a free boundary with application to the Pompeiu problem

Luis A. Caffarelli, Lavi Karp, Henrik Shahgholian

In the unit ball B(0,1), let $u$ and $Ω$ (a domain in $R$ ) solve the following overdetermined problem: $$Δu =χ_Ω\quad \hbox{in} B(0,1), \qquad 0 \in \partial Ω, \qquad u=|\nabla u…