Cylindrical optimal rearrangement problem leading to a new type obstacle problem

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4 Citations (Scopus)


An optimal rearrangement problem in a cylindrical domain Ω = D × (0, 1) is considered, under the constraint that the force function does not depend on the xn variable of the cylindrical axis. This leads to a new type of obstacle problem in the cylindrical domain Δu(x′, xn) = χ{v>0} (x′) + χ{v=0}(x′) [ νu(x′,0) + νu(x′, 1)] arising from minimization of the functional Ω1/2|u(x)|2 + χ{v>0} (x′)u(x) dx, where v(x′) = 01 u(x′, t)dt, and νu is the exterior normal derivative of u at the boundary. Several existence and regularity results are proven and it is shown that the comparison principle does not hold for minimizers.

Original languageEnglish
Pages (from-to)859-872
Number of pages14
JournalESAIM - Control, Optimisation and Calculus of Variations
Issue number2
Publication statusPublished - 1 Apr 2018


  • Obstacle problem
  • Rearrangements

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics


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