Abstract
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).
Original language | English (US) |
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Pages (from-to) | 183-200 |
Number of pages | 18 |
Journal | Mathematics in Science and Engineering |
Volume | 186 |
Issue number | C |
DOIs | |
State | Published - Jan 1 1992 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- General Engineering