TY - JOUR

T1 - Spatial critical points not moving along the heat flow II

T2 - The centrosymmetric case

AU - Magnanini, Rolando

AU - Sakaguchi, Shigeru

PY - 1999/4

Y1 - 1999/4

N2 - 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.

AB - 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.

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U2 - 10.1007/PL00004713

DO - 10.1007/PL00004713

M3 - Article

AN - SCOPUS:0033467469

VL - 230

SP - 695

EP - 712

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 4

ER -