A Serrin-type problem with partial knowledge of the domain

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

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