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Symmetry and asymmetry in a multi-phase overdetermined problem.
- Source :
- Interfaces & Free Boundaries; 2024, Vol. 26 Issue 3, p473-488, 16p
- Publication Year :
- 2024
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- SYMMETRY
IMPLICIT functions
TORSION
Subjects
Details
- Language :
- English
- ISSN :
- 14639963
- Volume :
- 26
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Interfaces & Free Boundaries
- Publication Type :
- Academic Journal
- Accession number :
- 178060765
- Full Text :
- https://doi.org/10.4171/IFB/512