Convex integral functionals
Convex integral functionals
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凸积分泛函
DOI：
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发表时间：
1997
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通讯作者：
Nikolaos S. Papageorgiou
中科院分区：
文献类型：
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作者：
Nikolaos S. Papageorgiou
研究了由正规凸被积函数确定的非线性积分泛函。首先，我们得到了它们的凸共轭、e-次微分（e > 0）和？方向导数然后，我们得到了一个必要的和充分的条件，存在的近似解的连续无穷卷积。我们还得到了保证条件期望算子和次微分算子的可积性的一般条件。最后，我们研究了随机集的条件期望。
We study nonlinear integral functionals determined by normal convex integrands. First we obtain expressions for their convex conjugate, their e-subdifferential (e > 0) and their ?-directional derivative. Then we derive a necessary and sufficient condition for the existence of an approximate solution for the continuous infimal convolution. We also obtain general conditions which guarantee the interchangeability of the conditional expectation and subdifferential operators. Finally we examine the conditional expectation of random sets.