PDE Comparison Principles for Robin Problems
Analysis of PDEs
2021-01-08 v2
Abstract
We compare the solutions of two Poisson problems in a spherical shell with Robin boundary conditions, one with given data, and one where the data has been cap symmetrized. When the Robin parameters are nonnegative, we show that the solution to the symmetrized problem has larger (increasing) convex means. We prove similar results on balls. We also prove a comparison principle on generalized cylinders with mixed boundary conditions (Neumann and Robin).
Cite
@article{arxiv.2011.15071,
title = {PDE Comparison Principles for Robin Problems},
author = {Jeffrey J. Langford},
journal= {arXiv preprint arXiv:2011.15071},
year = {2021}
}
Comments
Improved notation, new mixed results added, typos corrected