# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.332825

Arkiv for Matematik, 32, (2), 475-492, 1991.11
This paper deals with a free boundary porblem connected with the concept “quadrature surface”. Let Ω⊂$R$^{$n$}be a bounded domain with a$C$^{2}boundary and μ a measure compactly supported in Ω. Then we say ∂Ω is a quadrature surface with respect to μ if the following overdetermined Cauchy problem has a solution. $$\Delta u = - \mu in \Omega ,u = 0 and \frac{{\partial u}}{{\partial v}} = - 1 on \partial \Omega .$$
@inproceedings{henrik1991quadrature,
author={Henrik Shahgholian},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203544593510634},
booktitle={Arkiv for Matematik},
volume={32},
number={2},
pages={475-492},
year={1991},
}

Henrik Shahgholian. Quadrature surfaces as free boundaries. 1991. Vol. 32. In Arkiv for Matematik. pp.475-492. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203544593510634.