Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
844769 | Nonlinear Analysis: Theory, Methods & Applications | 2007 | 9 Pages |
Abstract
In this paper, we give a necessary and sufficient condition for a one-dimensional functional I(u)=∫01f(u̇(t))dt to satisfy the so-called (PS)-weak lower semicontinuity property on the space W1,p((0,1);Rm); that is, I(ū)≤lim infk→∞I(uk) for all uk⇀ū in W1,p((0,1);Rm) and I′(uk)→0I′(uk)→0 in W−1,pp−1((0,1);Rm). The result shows that in this case the property of (PS)-weak lower semicontinuity is in general not equivalent to convexity of the functional if m≥2m≥2.
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Authors
Daniel Vasiliu, Baisheng Yan,