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On quasiconvex equimeasurable rearrangement, a counterexample and an example. (English) Zbl 0848.35003

This paper concerns the existence of “quasiconvex equimeasurable rearrangement”, which reduces \(L^p\) gradient norm (with \(p> 1\)), preserves the distribution function and renders all level sets convex. The interaction between variational problems, partial differential equations encountered in analysis and in mathematical physics, and symmetrization and rearrangement techniques has proved a fruitful motivation for studying such a process.

MSC:

35A15 Variational methods applied to PDEs
35J50 Variational methods for elliptic systems
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