Note on Gagliardo's theorem " tr $W^{1,1}=L^1$"

Petru Mironescu (1)

1 EDPA - Équations aux dérivées partielles, analyse

We present a short proof of the fact, originally established by Gagliardo, that every function $f\in L^1({\mathbb R}^n)$ is the trace of a function $u\in W^{1,1}({\mathbb R}^n\times (0,\infty))$.

Mots clés: Gaglliado; trace

Domaines: Analyse classique [math.CA]

Petru Mironescu. Note on Gagliardo's theorem " tr $W^{1,1}=L^1$". Annals of the University of Bucharest. Mathematical series, 2015, 6 (LXIV) (1), pp.99--103. ⟨hal-01131162⟩