Quadrature surfaces as free boundaries

Henrik Shahgholian Department of Mathematics, Royal Institute of Technology

TBD mathscidoc: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. $$\Delta u = - \mu in \Omega ,u = 0 and \frac{{\partial u}}{{\partial v}} = - 1 on \partial \Omega .$$
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  title={Quadrature surfaces as free boundaries},
  author={Henrik Shahgholian},
  booktitle={Arkiv for Matematik},
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.
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