TY - JOUR
T1 - The (Non) Continuity of Symmetric Decreasing Rearrangement
AU - Almgren, Frederick J.
AU - Lieb, Elliott
PY - 1992/1/1
Y1 - 1992/1/1
N2 - The operation R of symmetric decreasing rearrangement maps W1,p(ℝn) to W1,p(ℝn). Even though it is norm decreasing we show that R is not continuous for n ≥ 2. The functions at which R is continuous are precisely characterized by a new property called co-area regularity. Every sufficiently differentiable function is co-area regular, and both the regular and the irregular functions are dense in W1,p(Rn).
AB - The operation R of symmetric decreasing rearrangement maps W1,p(ℝn) to W1,p(ℝn). Even though it is norm decreasing we show that R is not continuous for n ≥ 2. The functions at which R is continuous are precisely characterized by a new property called co-area regularity. Every sufficiently differentiable function is co-area regular, and both the regular and the irregular functions are dense in W1,p(Rn).
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U2 - 10.1016/S0076-5392(08)63380-9
DO - 10.1016/S0076-5392(08)63380-9
M3 - Article
AN - SCOPUS:77957028164
SN - 0076-5392
VL - 186
SP - 183
EP - 200
JO - Mathematics in Science and Engineering
JF - Mathematics in Science and Engineering
IS - C
ER -