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

Laurence, Peter; Stredulinsky, Edward

J. Reine Angew. Math. 447, 63-81 (1994).

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.

Reviewer: Sebastian Aniţa (Iaşi)

MSC:

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

Keywords:

symmetrization and rearrangement techniques