Extremizing temperature functions of rods with Robin boundary conditions

Författare

  • Jeffrey J. Langford Bucknell University, Department of Mathematics
  • Patrick McDonald New College of Florida, Division of Natural Science

Nyckelord:

Symmetrization, comparison theorems, Poisson's equation, Robin boundary conditions

Abstract

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.

 

Sektion
Articles

Publicerad

2022-05-12

Referera så här

Langford, J. J., & McDonald, P. (2022). Extremizing temperature functions of rods with Robin boundary conditions. Annales Fennici Mathematici, 47(2), 759–775. https://doi.org/10.54330/afm.119344