具有外场的infinite dimensional矢量势的平衡问题
Equilibrium problems for infinite dimensional vector potentials with external fields
摘要：
研究了局部紧空间中无限维非紧向量测度类上存在外场时的最小能量问题。这些分量是满足某些归一化假设的正测度（电荷），并由给定的闭集（板）支持，其符号为+1或-1，使得符号相反的集相互不相交，电荷的相互作用矩阵对应于电容器的静电解释。对所有满足Fuglede弱拓扑与强拓扑相容条件的正定核，建立了平衡测度存在的充分条件，并研究了它们的唯一性、淡紧和连续性.我们还得到了加权平衡势的变分不等式，指出了它们的特征性质，并分析了平衡常数的连续性。
英文摘要：
The study deals with a minimal energy problem in the presence of an external field over noncompact classes of vector measures of infinite dimension in a locally compact space. The components are positive measures (charges) satisfying certain normalizing assumptions and supported by given closed sets (plates) with the sign +1 or -1 prescribed such that oppositely signed sets are mutually disjoint, and the interaction matrix for the charges corresponds to an electrostatic interpretation of a condenser. For all positive definite kernels satisfying Fuglede's condition of consistency between the weak* and strong topologies, sufficient conditions for the existence of equilibrium measures are established and properties of their uniqueness, vague compactness, and continuity are studied. We also obtain variational inequalities for the weighted equilibrium potentials, single out their characteristic properties, and analyze continuity of the equilibrium constants.
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