Optimization problems for an energy functional with mass constraint revisited
Optimization problems for an energy functional with mass constraint revisited
复制标题
重新审视具有质量约束的能量泛函的优化问题
DOI：
10.1016/j.jmaa.2008.05.102
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发表时间：
2009
影响因子：
1.3
通讯作者：
A. Wagner
中科院分区：
文献类型：
--
作者：
C. Bandle;A. Wagner
在本文中，我们报告的变分问题的约束下的质量，这是出于扭转刚度和扭转蠕变。以下设备的Alt，Caffarelli和弗里德曼，我们对待，而不是一个问题，没有约束，但与惩罚条款。我们将完成[C]的一些结果。Bandle，A.瓦格纳，加权Sobolev常数的优化问题，计算。变种偏微分方程29（2007）481-507]，其中已经建立了Lipschitz连续最小值的存在性。特别是，我们证明了最佳形状的定性性质。
In this paper we report on a variational problem under a constraint on the mass which is motivated by the torsional rigidity and torsional creep. Following a device by Alt, Caffarelli and Friedman we treat instead a problem without constraint but with a penalty term. We will complete some of the results of [C. Bandle, A. Wagner, Optimization problems for weighted Sobolev constants, Calc. Var. Partial Differential Equations 29 (2007) 481–507] where the existence of a Lipschitz continuous minimizer has been established. In particular we prove qualitative properties of the optimal shape.