Spatial critical points not moving along the heat flow II: The centrosymmetric case

Rolando Magnanini, Shigeru Sakaguchi

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We consider solutions of initial-boundary value problems for the heat equation on bounded domains in ℝN, and their spatial critical points as in the previous paper [MS]. In Dirichlet, Neumann, and Robin homogeneous initial-boundary value problems on bounded domains, it is proved that if the origin is a spatial critical point never moving for sufficiently many compactly supported initial data being centrosymmetric with respect to the origin, then the domain must be centrosymmetric with respect to the origin. Furthermore, we consider spatial zero points instead of spatial critical points, and prove some similar symmetry theorems. Also, it is proved that these symmetry theorems hold for initial-boundary value problems for the wave equation.

Original languageEnglish
Pages (from-to)695-712
Number of pages18
JournalMathematische Zeitschrift
Volume230
Issue number4
DOIs
Publication statusPublished - 1999 Apr
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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