We prove that a nonlocal functional approximating the standard Dirichlet p-norm fails to decrease under two-point rearrangement. Furthermore, we get other properties related to this functional such as decay and compactness.
Nguyen, H., Squassina, M., Some remarks on rearrangement for nonlocal functionals, <<NONLINEAR ANALYSIS>>, 2017; (162): 1-12. [doi:10.1016/j.na.2017.06.007] [http://hdl.handle.net/10807/116454]
Some remarks on rearrangement for nonlocal functionals
Squassina, Marco
2017
Abstract
We prove that a nonlocal functional approximating the standard Dirichlet p-norm fails to decrease under two-point rearrangement. Furthermore, we get other properties related to this functional such as decay and compactness.
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