Lower semicontinuity in Sobolev spaces below the growth exponent of the integrand
Let there be given a non-negative, quasiconvex function F satisfying the growth condition lim supA→∞ F(A)/|A|p = 0 (*) for some p ∈ ] 1, ∞ [. For an open and bounded set Ω ⊂ ℝm, we show that if q≧ m-1/m p and q > 1, then the variational integral ℱ(u; Ω):= ∫Ω F(Du) dx is lower semicontinuous o...
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| 格式: | Journal article |
| 语言: | English |
| 出版: |
1997
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