Universal approximation of symmetrizations by polarizations
Jean Van Schaftingen · Proceedings of the American Mathematical Society · 2005
Any symmetrization (Schwarz, Steiner, cap or increasing rear- rangement) can be approximated by a universal sequence of polarizations which converges in L p \mathrm {L}^p norm for any admissible function in L p \mathrm {L}^p for 1 ≤ p > + ∞ 1 \le p > +\infty and uniformly for admissible continuous functions. A new Pólya-Szegö inequality is proved for the increasing rearrangement.