On the symmetric rearrangement of the gradient of a Sobolev function
Analysis of PDEs
2023-05-18 v2
Abstract
In this paper, we generalize a classical comparison result for solutions to Hamilton-Jacobi equations with Dirichlet boundary conditions, to solutions to Hamilton-Jacobi equations with non-zero boundary trace. As a consequence, we prove the isoperimetric inequality for the torsional rigidity (with Robin boundary conditions) and for other functionals involving such boundary conditions.
Keywords
Cite
@article{arxiv.2207.09129,
title = {On the symmetric rearrangement of the gradient of a Sobolev function},
author = {Vincenzo Amato and Andrea Gentile},
journal= {arXiv preprint arXiv:2207.09129},
year = {2023}
}