Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces
Brezis, Haïm ; Mironescu, Petru
HAL, hal-00747694 / Harvested from HAL
Text on HAL
Our main result is that, when $f$ is smooth and has bounded derivatives, and when $u$ belongs to the spaces $W^{s,p}$ and $W^{1,sp}$, the map $f(u)$ is in $W^{s,p}$.
Publié le : 2001-07-05
Classification:  paraproducts,  composition,  Sobolev spaces,  46E35 ; 46E39,  [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] 
@article{hal-00747694,
     author = {Brezis, Ha\"\i m and Mironescu, Petru},
     title = {Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00747694}
}

Brezis, Haïm; Mironescu, Petru. Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00747694/