| 某类多重积分变分问题的全局Lipschitz连续性 |
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| 引用本文： | 简怀玉.某类多重积分变分问题的全局Lipschitz连续性[J].怀化学院学报,1989(5). |
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| 作者姓名： | 简怀玉 |
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| 作者单位： | 怀化师专数学科 |
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| 摘 要： | 本文证明了:泛函在空间中最小点u的全局Lipschitz连续性,从而把文1]的局部结果推广到整体。这里F:M~(n×N)→R,F(p)≡F_1(p)+F_2(p),F_2是一个具有有界支集的有界函数,F_1是一可微函数,且在无穷远邻域内近于凸。作为推论,我们得到了文2]中的松驰最优设计问题解的全局Lipschitz连续性。
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| 关 键 词： | 多重变分问题 全局Lipschitz连续性 正规族 |
Global Lipschitz Continuity for Certain Problems in the Calculus of Variation of Multiple Integrals |
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| Abstract: | In this paper, global Lipschitz continuity for minimiscrs of functional,
I(φ)= ∫ F(Dφ)dx, in the spacc{φH1 (Ω, RN): φ = V on f1Ω} is proved, Thus
Ω
the local results in 1 ] is extended to the global. Where F: Ma×Nr3R, F(p) (?) F1 (P) + Ω(p), Ω is a bounded function with bounded support, F1 is differential and appropriately comvex. As a collarary, We prove the minimisers for the relaxed Optimal design problem, derived in 2 ] are global Lipschitz continuous. |
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