### Abstract

In previous papers [MS 1, 2], we considered stationary critical points of solutions of the initial-boundary value problems for the heat equation on bounded domains in ℝ^{N}, N ≧ 2. In [MS 1], we showed that a solution u has a stationary critical point O if and only if u satisfies a certain balance law with respect to O for any time. Furthermore, we proved necessary and sufficient conditions relating the symmetry of the domain to the initial data u_{0}; in this way, we gave a characterization of the ball in ℝ^{N} ([MS 1]) and of centrosymmetric domains ([MS 2]). In the present paper, we consider a rotation A_{d} by an angle 2π/d, d ≧ 2 for planar domains and give some necessary and some sufficient conditions on u_{0} which relate to domains invariant under A_{d}. We also establish some conjectures.

Original language | English |
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Pages (from-to) | 383-396 |

Number of pages | 14 |

Journal | Journal d'Analyse Mathematique |

Volume | 88 |

DOIs | |

Publication status | Published - 2002 |

### ASJC Scopus subject areas

- Analysis
- Mathematics(all)

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## Cite this

*Journal d'Analyse Mathematique*,

*88*, 383-396. https://doi.org/10.1007/BF02786582