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An inequality concerning rearrangements of functions and Hamilton-Jacobi equations. (English) Zbl 0787.35020
The authors prove an inequality concerning the decreasing rearrangement of functions. This inequality gives a comparison result between the viscosity solution of an initial boundary value problem for the Hamilton- Jacobi equation and the viscosity solution of the “symmetrized” problem.

35F10 Initial value problems for linear first-order PDEs
35A15 Variational methods applied to PDEs
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
26D20 Other analytical inequalities
35D99 Generalized solutions to partial differential equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
Full Text: DOI
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