C2-Lusin approximation of strongly convex functions
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Abstract We prove that if u : R n → R is strongly convex, then for every ε > 0 there is a strongly convex function v ∈ C 2 ( R n ) such that | { u ≠ v } | < ε and ∥ u − v ∥ ∞ < ε .
Date issued
2024-04-03Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Inventiones mathematicae
Publisher
Springer Berlin Heidelberg
Citation
Azagra, D., Drake, M. & Hajłasz, P. C2-Lusin approximation of strongly convex functions. Invent. math. 236, 1055–1082 (2024).
Version: Author's final manuscript