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arXiv · 2207.09129

On the symmetric rearrangement of the gradient of a Sobolev function

Vincenzo Amato·Andrea Gentile
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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.

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Vincenzo Amato, Andrea Gentile. 2023-05-17. On the symmetric rearrangement of the gradient of a Sobolev function. https://arxiv.org/abs/2207.09129

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