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monotone decreasing and relative rearrangements

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Numerical Approximations of the Relative Rearrangement:The piecewise linear case.Application to some Nonlocal Problems
Jean-Michel Rakotoson, Maria Luisa Seoane
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 34 / Issue 2 / March 2000

Published online by Cambridge University Press:

15 April 2002, pp. 477-499

Print publication:

March 2000
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We first prove an abstract result for a class of nonlocalproblems using fixed point method. We apply this result toequations revelant from plasma physic problems. These equationscontain terms like monotone or relative rearrangement of functions.So, we start the approximation study by using finite element todiscretize this nonstandard quantities. We end the paper by giving a numerical resolution of a model containing those terms.