A Serrin-type problem with partial knowledge of the domain

Abstract We present a quantitative estimate for the radially symmetric configuration concerning Serrin-type overdetermined problem torsional rigidity in bounded domain Ω ⊂ R N , when equation is known on  ∖ ω ¯ only, some open subset  ⋐ . The has concrete motivations optimal heating with malfunctioning, laminar flows and beams small inhomogeneities.