On a constrained variational problem with an arbitrary number of free boundaries
On a constrained variational problem with an arbitrary number of free boundaries
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关于具有任意数量自由边界的约束变分问题
DOI：
10.4171/ifb/18
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发表时间：
2000
影响因子：
1
通讯作者：
P. Tilli
中科院分区：
文献类型：
--
作者：
P. Tilli
研究了在所有水平集{u = li }具有指定的Lebesgue测度αi的函数u ∈ H1（H1）中Dirichlet积分的极小化问题.这个问题被引入与不混溶流体之间的界面模型。证明了在任意数量的水平集约束下极小解的存在性，并研究了其正则性。我们的技术包括扩大类的容许函数的整个空间H 1（λ），惩罚那些函数的水平集的措施远离那些需要的，事实上，我们研究的极小
We study the problem of minimizing the Dirichlet integral among all functions u ∈ H 1 (Ω) whose level sets {u = li } have prescribed Lebesgue measure αi . This problem was introduced in connection with a model for the interface between immiscible fluids. The existence of minimizers is proved with an arbitrary number of level-set constraints, and their regularity is investigated. Our technique consists in enlarging the class of admissible functions to the whole space H 1 (Ω), penalizing those functions whose level sets have measures far from those required; in fact, we study the minimizers of