Global Div-Curl lemma in negative Sobolev spaces

摘要

This paper studies the global version of the Div-Curl lemma in negative Sobolev spaces in bounded domains in R~3. We proved that for the two sequences {u_j}_(j=1)~∞and {v_j}_(j=1)~∞ converging to u and v weakly in L~r(Ω) and L~r (Ω), respectively, with r and r' being conjugate exponents and 1