A necessary and sufficient condition for the weak lower semicontinuity of one-dimensional non-local variational integrals
2006 ◽
Vol 136
(4)
◽
pp. 701-708
◽
Keyword(s):
In this short note we prove that the functional I : W1,p(J;R) → R defined by is sequentially weakly lower semicontinuous in W1,p(J,R) if and only if the symmetric part W+ of W is separately convex. We assume that W is real valued, continuous and bounded below by a constant, and that J is an open subinterval of R. We also show that the lower semicontinuous envelope of I cannot in general be obtained by replacing W by its separately convex hull Wsc.
1990 ◽
Vol 32
(2)
◽
pp. 180-192
◽
1990 ◽
Vol 42
(2)
◽
pp. 315-341
◽
1979 ◽
Vol 31
(2)
◽
pp. 255-263
◽
1973 ◽
Vol 25
(5)
◽
pp. 1078-1089
◽
1978 ◽
Vol 26
(1)
◽
pp. 31-45
◽
2018 ◽
Vol 6
(1)
◽
pp. 129-145
◽
1972 ◽
Vol 18
(2)
◽
pp. 129-136
◽
1981 ◽
Vol 89
(1-2)
◽
pp. 25-50
◽
1996 ◽
Vol 39
(3)
◽
pp. 275-283
◽