Symmetry and asymmetry in a multi-phase overdetermined problem
A celebrated theorem of Serrin asserts that one overdetermined condition on the boundary is enough to obtain radial symmetry in the so-called one-phase overdetermined torsion problem. It is also known that imposing just one overdetermined condition on the boundary is not enough to obtain radial symm...
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| Vydáno v: | Interfaces and free boundaries Ročník 26; číslo 3; s. 473 - 488 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
European Mathematical Society Publishing House
01.09.2024
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| Témata: | |
| ISSN: | 1463-9963, 1463-9971 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | A celebrated theorem of Serrin asserts that one overdetermined condition on the boundary is enough to obtain radial symmetry in the so-called one-phase overdetermined torsion problem. It is also known that imposing just one overdetermined condition on the boundary is not enough to obtain radial symmetry in the corresponding multi-phase overdetermined problem. In this paper we show that, in order to obtain radial symmetry in the two-phase overdetermined torsion problem, two overdetermined conditions are needed. Moreover, it is noteworthy that this pattern does not extend to multi-phase problems with three or more layers, for which we show the existence of nonradial configurations satisfying countably infinitely many overdetermined conditions on the outer boundary. |
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| ISSN: | 1463-9963 1463-9971 |
| DOI: | 10.4171/ifb/512 |