Abstract
The aim of this note is to show that Alexandrov solutions of the Monge-Ampère equation, with right-hand side bounded away from zero and infinity, converge strongly in W2,1 loc if their right-hand sides converge strongly in L1 loc. As a corollary, we deduce strong W1,1 loc stability of optimal transport maps.
Original language | English (US) |
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Pages (from-to) | 993-1000 |
Number of pages | 8 |
Journal | Analysis and PDE |
Volume | 6 |
Issue number | 4 |
DOIs | |
State | Published - 2013 |
Keywords
- Monge-Ampère
- Sobolev convergence
- Stability
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Applied Mathematics