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

Voir la notice de l'article provenant de la source Journal.fi

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 
@article{AFM_2022_47_2_a7,
     author = {Jeffrey J. Langford and Patrick McDonald},
     title = {Extremizing temperature functions of rods with {Robin} boundary conditions},
     journal = {Annales Fennici Mathematici},
     pages = {759--775},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2022},
     doi = {10.54330/afm.119344},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.54330/afm.119344/}
}
TY  - JOUR
AU  - Jeffrey J. Langford
AU  - Patrick McDonald
TI  - Extremizing temperature functions of rods with Robin boundary conditions
JO  - Annales Fennici Mathematici
PY  - 2022
SP  - 759
EP  - 775
VL  - 47
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.54330/afm.119344/
DO  - 10.54330/afm.119344
LA  - en
ID  - AFM_2022_47_2_a7
ER  - 
%0 Journal Article
%A Jeffrey J. Langford
%A Patrick McDonald
%T Extremizing temperature functions of rods with Robin boundary conditions
%J Annales Fennici Mathematici
%D 2022
%P 759-775
%V 47
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.54330/afm.119344/
%R 10.54330/afm.119344
%G en
%F AFM_2022_47_2_a7
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. http://geodesic.mathdoc.fr/articles/10.54330/afm.119344/

Cité par Sources :