Another look at Sobolev spaces

Abstract

The standard seminorm in the space $W^{s,p}$, with $s$<$1$, does not converge, when $s$ approaches $1$, to the corresponding $W^{1,p}$ seminorm. We prove that continuity is restored provided we multiply the $W^{s,p}$ seminorm by an appropriate factor.

Locations

• CiteSeer X (The Pennsylvania State University) - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF