A necessary and sufficient condition for the weak lower semicontinuity of one-dimensional non-local variational integrals
A necessary and sufficient condition for the weak lower semicontinuity of one-dimensional non-local variational integrals
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一维非局部变分积分弱下半连续性的充要条件
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
P. Pedregal
中科院分区：
文献类型：
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作者：
J. Bevan;P. Pedregal
本文证明了由定义的泛函I：W1，p（J;R）→ R在W1，p（J，R）中是序列弱下连续的当且仅当W的对称部分W+是分离凸的.我们假设W是真实的值的、连续的且被一个常数下界的，并且J是R的一个开子区间。我们还表明，较低的连续包络的I不能在一般情况下，通过取代W的单独凸船体WSC。
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.