Abstract
We prove a strong form of the quantitative Sobolev inequality in Rn for p ≥ 2, where the deficit of a function u ∈ W 1,p controls k∇u−∇vkLp for an extremal function v in the Sobolev inequality.
Original language | English (US) |
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Pages (from-to) | 319-354 |
Number of pages | 36 |
Journal | Journal of the European Mathematical Society |
Volume | 21 |
Issue number | 2 |
DOIs | |
State | Published - 2019 |
Keywords
- Quantitative inequalities
- Sobolev inequality
- Stability
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics