Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 1103–1109

A NOTE ON LUSIN'S CONDITION (N) FOR W_loc^1,n-MAPPINGS WITH CONVEX POTENTIALS

Diego Maldonado

Kansas State University, Department of Mathematics
138 Cardwell Hall, Manhattan, KS-66506, U.S.A.; dmaldona 'at' math.ksu.edu

Abstract. Given an open convex set Ω ⊂ Rⁿ and a convex function u ∈ W_loc^2,n(Ω), a short proof of the fact that |∇u(E)| = 0 for every subset E ⊂ Ω with |E| = 0 is presented.

2010 Mathematics Subject Classification: Primary 26B25, 26B10; Secondary 46E35, 28A75.

Key words: Sobolev mappings with convex potentials, Monge–Ampère measure, area formulas.

Reference to this article: D. Maldonado: A note on Lusin's condition (N) for W_loc^1,n-mappings with convex potentials. Ann. Acad. Sci. Fenn. Math. 45 (2020), 1103–1109.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4555

A NOTE ON LUSIN'S CONDITION (N) FOR Wloc1,n-MAPPINGS WITH CONVEX POTENTIALS

Diego Maldonado

A NOTE ON LUSIN'S CONDITION (N) FOR W_loc^1,n-MAPPINGS WITH CONVEX POTENTIALS