Geodesic
Extremizing temperature functions of rods with Robin boundary conditions
Jeffrey J. Langford1 ; Patrick McDonald2
1Bucknell University, Department of Mathematics
2New College of Florida, Division of Natural Science
Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 759-775

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We compare the solutions of two one-dimensional Poisson problems on an interval with Robin boundary conditions, one with given data, and one where the data has been symmetrized. When the Robin parameter is positive and the symmetrization is symmetric decreasing rearrangement, we prove that the solution to the symmetrized problem has larger increasing convex means. When the Robin parameter equals zero (so that we have Neumann boundary conditions) and the symmetrization is decreasing rearrangement, we similarly show that the solution to the symmetrized problem has larger convex means.  
DOI : 10.54330/afm.119344
Keywords: Symmetrization, comparison theorems, Poisson's equation, Robin boundary conditions

Jeffrey J. Langford  1   ; Patrick McDonald  2

1 Bucknell University, Department of Mathematics
2 New College of Florida, Division of Natural Science 
Jeffrey J. Langford; Patrick McDonald. Extremizing temperature functions of rods with Robin boundary conditions. Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 759-775. doi: 10.54330/afm.119344
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