外场约束能量问题
Constrained energy problems with external fields
摘要：
给定局部紧空间中的一个正定核，我们研究了一类非负Radon测度在外场存在下的最小能量问题，这些非负Radon测度由给定的非紧闭集支持，满足一定的规范化假设，并且不超过作为约束的固定测度.在一般的假设下，我们建立了极小化测度的存在性，并分析了它在弱 * 和强拓扑中的连续性。我们也给出了一个极小化测度的加权势的描述，并挑选出它的特征性质。这样的结果大多是新的，即使是经典的内核，这是重要的应用。
英文摘要：
Given a positive definite kernel in a locally compact space, we study a minimal energy problem in the presence of an external field over the class of all nonnegative Radon measures that are supported by a given closed noncompact set, satisfy certain normalizing assumptions, and do not exceed a fixed measure serving as a constraint. Under general assumptions, we establish the existence of a minimizing measure and analyze its continuity properties in the weak* and strong topologies when the set and the constraint are both varied. We also give a description of the weighted potential of a minimizing measure and single out its characteristic properties. Such results are mostly new even for classical kernels, which is important in applications.
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