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On the symmetric rearrangement of the gradient of a Sobolev function (2207.09129v2)
Published 19 Jul 2022 in math.AP
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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