Zusammenfassung
It is shown that u(k) . v(k) converges weakly to u . v if u(k) -> u weakly in L-P and v(k) -> v weakly in L-q with p, q is an element of (1, infinity), 1/p + 1/q = 1, under the additional assumptions that the sequences div u(k) and curl v(k) are compact in the dual space of W-0(1.infinity) and that u(k) . v(k) is equi-integrable. The main point is that we only require equi-integrability of the ...
Zusammenfassung
It is shown that u(k) . v(k) converges weakly to u . v if u(k) -> u weakly in L-P and v(k) -> v weakly in L-q with p, q is an element of (1, infinity), 1/p + 1/q = 1, under the additional assumptions that the sequences div u(k) and curl v(k) are compact in the dual space of W-0(1.infinity) and that u(k) . v(k) is equi-integrable. The main point is that we only require equi-integrability of the scalar product u(k) . v(k) and not of the individual sequences. (C) 2010 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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