### Abstract

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

Original language | English |
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Journal | arXiv preprint |

Publication status | Submitted - 11 May 2020 |

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## Cite this

Dipierro, S., Poggesi, G., & Valdinoci, E. (2020). A Serrin-type problem with partial knowledge of the domain. Manuscript submitted for publication.